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<div class="section end-of-chapter" id="fwk-redden-ch08_s06" version="5.0" lang="en">
<h2 class="title editable block">
<span class="title-prefix">8.6</span> Review Exercises and Sample Exam</h2>
<div class="qandaset block" id="fwk-redden-ch08_s06_qs01" defaultlabel="number">
<h3 class="title">Review Exercises</h3>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd01">
<h3 class="title">Distance, Midpoint, and the Parabola</h3>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd01_qd01">
<p class="para" id="fwk-redden-ch08_s06_qs01_p01"><strong class="emphasis bold">Calculate the distance and midpoint between the given two points.</strong></p>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa01">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p02"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1419" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>0</mn><mo>,</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1420" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>4</mn><mo>,</mo><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa02">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p04"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1422" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>6</mn><mo>,</mo><mn>0</mn></mrow><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1423" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>2</mn><mo>,</mo><mo>−</mo><mn>6</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa03">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p06"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1425" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>2</mn><mo>,</mo><mn>4</mn></mrow><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1426" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>6</mn><mo>,</mo><mo>−</mo><mn>8</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa04">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p08"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1429" display="inline"><mrow><mrow><mo>(</mo><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1430" display="inline"><mrow><mrow><mo>(</mo><mrow><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>,</mo><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa05">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p10"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1433" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>0</mn><mo>,</mo><mo>−</mo><mn>3</mn><msqrt><mn>2</mn></msqrt></mrow><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1434" display="inline"><mrow><mrow><mo>(</mo><mrow><msqrt><mn>5</mn></msqrt><mo>,</mo><mo>−</mo><mn>4</mn><msqrt><mn>2</mn></msqrt></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa06">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p12"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1437" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>5</mn><msqrt><mn>3</mn></msqrt><mo>,</mo><msqrt><mn>6</mn></msqrt></mrow><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1438" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>3</mn><msqrt><mn>3</mn></msqrt><mo>,</mo><msqrt><mn>6</mn></msqrt></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd01_qd02" start="7">
<p class="para" id="fwk-redden-ch08_s06_qs01_p14"><strong class="emphasis bold">Determine the area of a circle whose diameter is defined by the given two points.</strong></p>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa07">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p15"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1441" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>3</mn><mo>,</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1442" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>3</mn><mo>,</mo><mo>−</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa08">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p17"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1444" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>2</mn><mo>,</mo><mo>−</mo><mn>9</mn></mrow><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1445" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>10</mn><mo>,</mo><mo>−</mo><mn>15</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa09">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p19"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1447" display="inline"><mrow><mrow><mo>(</mo><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>,</mo><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1448" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>,</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa10">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p21"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1450" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>,</mo><mo>−</mo><mn>2</mn><msqrt><mn>2</mn></msqrt></mrow><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1451" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>0</mn><mo>,</mo><mo>−</mo><mn>4</mn><msqrt><mn>2</mn></msqrt></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd01_qd03" start="11">
<p class="para" id="fwk-redden-ch08_s06_qs01_p23"><strong class="emphasis bold">Rewrite in standard form and give the vertex.</strong></p>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa11">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p24"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1453" display="inline"><mrow><mi>y</mi><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>10</mn><mi>x</mi><mo>+</mo><mn>33</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa12">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p26"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1456" display="inline"><mrow><mi>y</mi><mo>=</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>x</mi><mo>−</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa13">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p28"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1459" display="inline"><mrow><mi>y</mi><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>3</mn><mi>x</mi><mo>−</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa14">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p30"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1462" display="inline"><mrow><mi>y</mi><mo>=</mo><mo>−</mo><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mi>x</mi><mo>−</mo><mn>2</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa15">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p32"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1465" display="inline"><mrow><mi>x</mi><mo>=</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>10</mn><mi>y</mi><mo>+</mo><mn>10</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa16">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p34"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1468" display="inline"><mrow><mi>x</mi><mo>=</mo><mn>3</mn><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn><mi>y</mi><mo>+</mo><mn>7</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa17">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p36"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1471" display="inline"><mrow><mi>x</mi><mo>=</mo><mo>−</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mi>y</mi><mo>−</mo><mn>3</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa18">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p38"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1474" display="inline"><mrow><mi>x</mi><mo>=</mo><mn>5</mn><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>5</mn><mi>y</mi><mo>+</mo><mn>2</mn></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd01_qd04" start="19">
<p class="para" id="fwk-redden-ch08_s06_qs01_p40"><strong class="emphasis bold">Rewrite in standard form and graph. Be sure to find the vertex and all intercepts.</strong></p>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa19">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p41"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1477" display="inline"><mrow><mi>y</mi><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>20</mn><mi>x</mi><mo>+</mo><mn>75</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa20">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p43"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1479" display="inline"><mrow><mi>y</mi><mo>=</mo><mo>−</mo><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>10</mn><mi>x</mi><mo>+</mo><mn>75</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa21">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p45"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1481" display="inline"><mrow><mi>y</mi><mo>=</mo><mo>−</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>12</mn><mi>x</mi><mo>−</mo><mn>24</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa22">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p47"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1483" display="inline"><mrow><mi>y</mi><mo>=</mo><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>6</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa23">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p49"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1485" display="inline"><mrow><mi>x</mi><mo>=</mo><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>10</mn><mi>y</mi><mo>+</mo><mn>16</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa24">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p51"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1487" display="inline"><mrow><mi>x</mi><mo>=</mo><mo>−</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>y</mi><mo>+</mo><mn>12</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa25">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p53"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1489" display="inline"><mrow><mi>x</mi><mo>=</mo><mo>−</mo><mn>4</mn><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn><mi>y</mi></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa26">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p55"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1491" display="inline"><mrow><mi>x</mi><mo>=</mo><mn>9</mn><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>18</mn><mi>y</mi><mo>+</mo><mn>12</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa27">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p57"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1493" display="inline"><mrow><mi>x</mi><mo>=</mo><mo>−</mo><mn>4</mn><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>y</mi><mo>+</mo><mn>2</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa28">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p59"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1495" display="inline"><mrow><mi>x</mi><mo>=</mo><mo>−</mo><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>5</mn><mi>y</mi><mo>+</mo><mn>2</mn></mrow></math></span></p>
</div>
</li>
</ol>
</ol>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd02">
<h3 class="title">Circles</h3>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd02_qd01" start="29">
<p class="para" id="fwk-redden-ch08_s06_qs01_p61"><strong class="emphasis bold">Determine the center and radius given the equation of a circle in standard form.</strong></p>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa29">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p62"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1497" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>6</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>9</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa30">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p64"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1500" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>8</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>−</mo><mn>10</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa31">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p66"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1503" display="inline"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>5</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa32">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p68"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1506" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mfrac><mn>3</mn><mn>8</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>+</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd02_qd02" start="33">
<p class="para" id="fwk-redden-ch08_s06_qs01_p70"><strong class="emphasis bold">Determine standard form for the equation of the circle:</strong></p>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa33">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p71">Center <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1509" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>7</mn><mo>,</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow></math></span> with radius <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1510" display="inline"><mrow><mi>r</mi><mo>=</mo><mn>10</mn></mrow><mo>.</mo></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa34">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p73">Center <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1512" display="inline"><mrow><mrow><mo>(</mo><mrow><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>,</mo><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></math></span> with radius <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1513" display="inline"><mrow><mi>r</mi><mo>=</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow><mo>.</mo></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa35">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p75">Center <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1515" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>0</mn><mo>,</mo><mo>−</mo><mn>5</mn></mrow><mo>)</mo></mrow></mrow></math></span> with radius <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1516" display="inline"><mrow><mi>r</mi><mo>=</mo><mn>2</mn><msqrt><mn>7</mn></msqrt></mrow><mo>.</mo></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa36">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p77">Center <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1518" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>,</mo><mn>0</mn></mrow><mo>)</mo></mrow></mrow></math></span> with radius <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1519" display="inline"><mrow><mi>r</mi><mo>=</mo><mfrac><mrow><mn>5</mn><msqrt><mn>3</mn></msqrt></mrow><mn>2</mn></mfrac></mrow><mo>.</mo></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa37">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p79">Circle whose diameter is defined by <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1521" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>4</mn><mo>,</mo><mn>10</mn></mrow><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1522" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>2</mn><mo>,</mo><mn>8</mn></mrow><mo>)</mo></mrow></mrow><mo>.</mo></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa38">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p81">Circle whose diameter is defined by <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1524" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>3</mn><mo>,</mo><mo>−</mo><mn>6</mn></mrow><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1525" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>0</mn><mo>,</mo><mo>−</mo><mn>4</mn></mrow><mo>)</mo></mrow></mrow><mo>.</mo></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd02_qd03" start="39">
<p class="para" id="fwk-redden-ch08_s06_qs01_p83"><strong class="emphasis bold">Find the <em class="emphasis">x</em>- and <em class="emphasis">y</em>-intercepts.</strong></p>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa39">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p84"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1527" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>+</mo><mn>5</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>=</mo><mn>16</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa40">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p86"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1529" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>=</mo><mn>4</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa41">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p88"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1531" display="inline"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>−</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>=</mo><mn>20</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa42">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p90"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1534" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>+</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>=</mo><mn>8</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa43">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p92"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1535" display="inline"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>12</mn><mi>y</mi><mo>+</mo><mn>27</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa44">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p94"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1538" display="inline"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi><mo>+</mo><mn>1</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd02_qd04" start="45">
<p class="para" id="fwk-redden-ch08_s06_qs01_p96"><strong class="emphasis bold">Graph.</strong></p>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa45">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p97"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1541" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>8</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>−</mo><mn>6</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>=</mo><mn>4</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa46">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p99"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1542" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>20</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>+</mo><mfrac><mrow><mn>15</mn></mrow><mn>2</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>=</mo><mfrac><mrow><mn>225</mn></mrow><mn>4</mn></mfrac></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa47">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p101"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1543" display="inline"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>24</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa48">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p103"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1544" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa49">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p105"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1545" display="inline"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>−</mo><mn>7</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>=</mo><mn>27</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa50">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p107"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1546" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>=</mo><mn>2</mn></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd02_qd05" start="51">
<p class="para" id="fwk-redden-ch08_s06_qs01_p109"><strong class="emphasis bold">Rewrite in standard form and graph.</strong></p>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa51">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p110"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1547" display="inline"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>6</mn><mi>x</mi><mo>+</mo><mn>4</mn><mi>y</mi><mo>−</mo><mn>3</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa52">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p112"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1549" display="inline"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mi>x</mi><mo>−</mo><mn>10</mn><mi>y</mi><mo>+</mo><mn>16</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa53">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p114"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1551" display="inline"><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><mi>x</mi><mo>−</mo><mn>6</mn><mi>y</mi><mo>−</mo><mn>3</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa54">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p116"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1553" display="inline"><mrow><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mi>y</mi><mo>+</mo><mn>1</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa55">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p118"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1555" display="inline"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>5</mn><mi>x</mi><mo>+</mo><mi>y</mi><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa56">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p120"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1557" display="inline"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn><mi>x</mi><mo>−</mo><mn>8</mn><mi>y</mi><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
</ol>
</ol>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd03">
<h3 class="title">Ellipses</h3>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd03_qd01" start="57">
<p class="para" id="fwk-redden-ch08_s06_qs01_p122"><strong class="emphasis bold">Given the equation of an ellipse in standard form, determine its center, orientation, major radius, and minor radius.</strong></p>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa57">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p123"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1559" display="inline"><mrow><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>12</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mrow><mn>16</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>−</mo><mn>10</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mn>4</mn></mfrac><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa58">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p125"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1561" display="inline"><mrow><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mn>3</mn></mfrac><mo>+</mo><mfrac><mrow><msup><mi>y</mi><mn>2</mn></msup></mrow><mrow><mn>25</mn></mrow></mfrac><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa59">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p127"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1564" display="inline"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>−</mo><mn>5</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mrow><mn>12</mn></mrow></mfrac><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa60">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p129"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1567" display="inline"><mrow><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>8</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mn>5</mn></mfrac><mo>+</mo><mfrac><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>+</mo><mn>8</mn></mrow><mo>)</mo></mrow></mrow><mrow><mn>18</mn></mrow></mfrac><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd03_qd02" start="61">
<p class="para" id="fwk-redden-ch08_s06_qs01_p131"><strong class="emphasis bold">Determine the standard form for the equation of the ellipse given the following information.</strong></p>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa61">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p132">Center <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1571" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>0</mn><mo>,</mo><mo>−</mo><mn>4</mn></mrow><mo>)</mo></mrow></mrow></math></span> with <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1572" display="inline"><mrow><mi>a</mi><mo>=</mo><mn>3</mn></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1573" display="inline"><mrow><mi>b</mi><mo>=</mo><mn>4</mn></mrow><mo>.</mo></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa62">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p134">Center <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1575" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>3</mn><mo>,</mo><mn>8</mn></mrow><mo>)</mo></mrow></mrow></math></span> with <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1576" display="inline"><mrow><mi>a</mi><mo>=</mo><mn>1</mn></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1577" display="inline"><mrow><mi>b</mi><mo>=</mo><msqrt><mn>7</mn></msqrt></mrow><mo>.</mo></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa63">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p136">Center <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1579" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow><mo>)</mo></mrow></mrow></math></span> with <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1580" display="inline"><mrow><mi>a</mi><mo>=</mo><mn>5</mn></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1581" display="inline"><mrow><mi>b</mi><mo>=</mo><msqrt><mn>2</mn></msqrt></mrow><mo>.</mo></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa64">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p138">Center <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1583" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>10</mn><mo>,</mo><mo>−</mo><mn>30</mn></mrow><mo>)</mo></mrow></mrow></math></span> with <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1584" display="inline"><mrow><mi>a</mi><mo>=</mo><mn>10</mn></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1585" display="inline"><mrow><mi>b</mi><mo>=</mo><mn>1</mn></mrow><mo>.</mo></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd03_qd03" start="65">
<p class="para" id="fwk-redden-ch08_s06_qs01_p140"><strong class="emphasis bold">Find the <em class="emphasis">x</em>- and <em class="emphasis">y</em>-intercepts.</strong></p>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa65">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p141"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1587" display="inline"><mrow><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mn>4</mn></mfrac><mo>+</mo><mfrac><mrow><msup><mi>y</mi><mn>2</mn></msup></mrow><mn>9</mn></mfrac><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa66">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p143"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1591" display="inline"><mrow><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mn>2</mn></mfrac><mo>+</mo><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mn>3</mn></mfrac><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa67">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p145"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1594" display="inline"><mrow><mn>5</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>20</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa68">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p147"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1597" display="inline"><mrow><mn>5</mn><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><mn>6</mn><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>120</mn></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd03_qd04" start="69">
<p class="para" id="fwk-redden-ch08_s06_qs01_p149"><strong class="emphasis bold">Graph.</strong></p>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa69">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p150"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1600" display="inline"><mrow><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>10</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mrow><mn>25</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>+</mo><mn>5</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mn>4</mn></mfrac><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa70">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p152"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1601" display="inline"><mrow><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mn>9</mn></mfrac><mo>+</mo><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>−</mo><mn>8</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mrow><mn>36</mn></mrow></mfrac><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa71">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p154"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1602" display="inline"><mrow><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mn>4</mn></mfrac><mo>+</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>−</mo><mfrac><mn>7</mn><mn>2</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa72">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p156"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1603" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><mfrac><mrow><msup><mi>y</mi><mn>2</mn></msup></mrow><mn>4</mn></mfrac><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa73">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p158"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1604" display="inline"><mrow><mfrac><mrow><msup><mi>x</mi><mn>2</mn></msup></mrow><mn>2</mn></mfrac><mo>+</mo><mfrac><mrow><msup><mi>y</mi><mn>2</mn></msup></mrow><mn>5</mn></mfrac><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa74">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p160"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1605" display="inline"><mrow><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mn>8</mn></mfrac><mo>+</mo><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>−</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mrow><mn>12</mn></mrow></mfrac><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd03_qd05" start="75">
<p class="para" id="fwk-redden-ch08_s06_qs01_p162"><strong class="emphasis bold">Rewrite in standard form and graph.</strong></p>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa75">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p163"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1606" display="inline"><mrow><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>9</mn><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>8</mn><mi>x</mi><mo>+</mo><mn>90</mn><mi>y</mi><mo>+</mo><mn>193</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa76">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p165"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1608" display="inline"><mrow><mn>9</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>108</mn><mi>x</mi><mo>−</mo><mn>80</mn><mi>y</mi><mo>+</mo><mn>580</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa77">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p167"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1610" display="inline"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>9</mn><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>6</mn><mi>x</mi><mo>+</mo><mn>108</mn><mi>y</mi><mo>+</mo><mn>324</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa78">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p169"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1612" display="inline"><mrow><mn>25</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>350</mn><mi>x</mi><mo>−</mo><mn>8</mn><mi>y</mi><mo>+</mo><mn>1,216</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa79">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p171"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1614" display="inline"><mrow><mn>8</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>16</mn><mi>x</mi><mo>−</mo><mn>36</mn><mi>y</mi><mo>−</mo><mn>13</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa80">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p173"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1616" display="inline"><mrow><mn>10</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>50</mn><mi>x</mi><mo>+</mo><mn>14</mn><mi>y</mi><mo>+</mo><mn>7</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
</ol>
</ol>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd04">
<h3 class="title">Hyperbolas</h3>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd04_qd01" start="81">
<p class="para" id="fwk-redden-ch08_s06_qs01_p175"><strong class="emphasis bold">Given the equation of a hyperbola in standard form, determine its center, which way the graph opens, and the vertices.</strong></p>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa81">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p176"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1618" display="inline"><mrow><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>10</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mn>4</mn></mfrac><mo>−</mo><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>+</mo><mn>5</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mrow><mn>16</mn></mrow></mfrac><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa82">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p178"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1622" display="inline"><mrow><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>7</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mn>2</mn></mfrac><mo>−</mo><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>−</mo><mn>8</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mn>8</mn></mfrac><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa83">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p180"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1626" display="inline"><mrow><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>−</mo><mn>20</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mn>3</mn></mfrac><mo>−</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>15</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa84">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p182"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1630" display="inline"><mrow><mn>3</mn><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>12</mn><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>=</mo><mn>36</mn></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd04_qd02" start="85">
<p class="para" id="fwk-redden-ch08_s06_qs01_p184"><strong class="emphasis bold">Determine the standard form for the equation of the hyperbola.</strong></p>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa85">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p185">Center <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1634" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>25</mn><mo>,</mo><mn>10</mn></mrow><mo>)</mo></mrow></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1635" display="inline"><mrow><mi>a</mi><mo>=</mo><mn>3</mn></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1636" display="inline"><mrow><mi>b</mi><mo>=</mo><msqrt><mn>5</mn></msqrt></mrow></math></span>, opens up and down.</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa86">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p187">Center <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1638" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>9</mn><mo>,</mo><mo>−</mo><mn>12</mn></mrow><mo>)</mo></mrow></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1639" display="inline"><mrow><mi>a</mi><mo>=</mo><mn>5</mn><msqrt><mn>3</mn></msqrt></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1640" display="inline"><mrow><mi>b</mi><mo>=</mo><mn>7</mn></mrow></math></span>, opens left and right.</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa87">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p189">Center <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1642" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>4</mn><mo>,</mo><mn>0</mn></mrow><mo>)</mo></mrow></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1643" display="inline"><mrow><mi>a</mi><mo>=</mo><mn>1</mn></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1644" display="inline"><mrow><mi>b</mi><mo>=</mo><mn>6</mn></mrow></math></span>, opens left and right.</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa88">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p191">Center <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1646" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>2</mn><mo>,</mo><mo>−</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1647" display="inline"><mrow><mi>a</mi><mo>=</mo><mn>10</mn><msqrt><mn>2</mn></msqrt></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1648" display="inline"><mrow><mi>b</mi><mo>=</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></mrow></math></span>, opens up and down.</p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd04_qd03" start="89">
<p class="para" id="fwk-redden-ch08_s06_qs01_p193"><strong class="emphasis bold">Find the <em class="emphasis">x</em>- and <em class="emphasis">y</em>-intercepts.</strong></p>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa89">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p194"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1650" display="inline"><mrow><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mn>4</mn></mfrac><mo>−</mo><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>+</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mn>9</mn></mfrac><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa90">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p196"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1652" display="inline"><mrow><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mn>8</mn></mfrac><mo>−</mo><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>−</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mrow><mn>12</mn></mrow></mfrac><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa91">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p198"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1655" display="inline"><mrow><mn>4</mn><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>−</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>−</mo><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mn>16</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa92">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p200"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1659" display="inline"><mrow><mn>6</mn><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>−</mo><mn>3</mn><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>=</mo><mn>18</mn></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd04_qd04" start="93">
<p class="para" id="fwk-redden-ch08_s06_qs01_p202"><strong class="emphasis bold">Graph.</strong></p>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa93">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p203"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1661" display="inline"><mrow><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>10</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mrow><mn>25</mn></mrow></mfrac><mo>−</mo><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>+</mo><mn>5</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mrow><mn>100</mn></mrow></mfrac><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa94">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p205"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1662" display="inline"><mrow><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>4</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mn>4</mn></mfrac><mo>−</mo><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>−</mo><mn>8</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mrow><mn>16</mn></mrow></mfrac><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa95">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p207"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1663" display="inline"><mrow><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>−</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mn>9</mn></mfrac><mo>−</mo><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>6</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mrow><mn>81</mn></mrow></mfrac><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa96">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p209"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1664" display="inline"><mrow><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mn>4</mn></mfrac><mo>−</mo><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mrow><mn>25</mn></mrow></mfrac><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa97">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p211"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1665" display="inline"><mrow><mfrac><mrow><msup><mi>y</mi><mn>2</mn></msup></mrow><mrow><mn>27</mn></mrow></mfrac><mo>−</mo><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mn>9</mn></mfrac><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa98">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p213"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1666" display="inline"><mrow><mfrac><mrow><msup><mi>x</mi><mn>2</mn></msup></mrow><mn>2</mn></mfrac><mo>−</mo><mfrac><mrow><msup><mi>y</mi><mn>2</mn></msup></mrow><mn>3</mn></mfrac><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd04_qd05" start="99">
<p class="para" id="fwk-redden-ch08_s06_qs01_p215"><strong class="emphasis bold">Rewrite in standard form and graph.</strong></p>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa99">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p216"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1667" display="inline"><mrow><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>9</mn><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>8</mn><mi>x</mi><mo>−</mo><mn>90</mn><mi>y</mi><mo>−</mo><mn>257</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa100">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p218"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1669" display="inline"><mrow><mn>9</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>108</mn><mi>x</mi><mo>+</mo><mn>16</mn><mi>y</mi><mo>+</mo><mn>224</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa101">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p220"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1671" display="inline"><mrow><mn>25</mn><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>100</mn><mi>y</mi><mo>+</mo><mn>50</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa102">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p222"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1673" display="inline"><mrow><mn>3</mn><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><mi>x</mi><mo>−</mo><mn>10</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa103">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p224"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1675" display="inline"><mrow><mn>8</mn><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>12</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>24</mn><mi>y</mi><mo>−</mo><mn>12</mn><mi>x</mi><mo>−</mo><mn>33</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa104">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p226"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1677" display="inline"><mrow><mn>4</mn><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>16</mn><mi>y</mi><mo>−</mo><mn>28</mn><mi>x</mi><mo>−</mo><mn>37</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd04_qd06" start="105">
<p class="para" id="fwk-redden-ch08_s06_qs01_p228"><strong class="emphasis bold">Identify the conic sections and rewrite in standard form.</strong></p>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa105">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p229"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1679" display="inline"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><mi>x</mi><mo>−</mo><mn>8</mn><mi>y</mi><mo>+</mo><mn>16</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa106">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p231"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1681" display="inline"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>x</mi><mo>−</mo><mn>24</mn><mi>y</mi><mo>+</mo><mn>74</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa107">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p233"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1683" display="inline"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>6</mn><mi>x</mi><mo>−</mo><mn>4</mn><mi>y</mi><mo>+</mo><mn>3</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa108">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p235"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1685" display="inline"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>y</mi><mo>−</mo><mn>10</mn><mi>x</mi><mo>+</mo><mn>22</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa109">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p237"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1687" display="inline"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>12</mn><mi>x</mi><mo>+</mo><mn>24</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa110">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p239"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1689" display="inline"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>10</mn><mi>y</mi><mo>+</mo><mn>22</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa111">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p241"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1691" display="inline"><mrow><mn>4</mn><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>20</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>16</mn><mi>y</mi><mo>+</mo><mn>20</mn><mi>x</mi><mo>−</mo><mn>9</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa112">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p243"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1693" display="inline"><mrow><mn>16</mn><mi>x</mi><mo>−</mo><mn>16</mn><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>24</mn><mi>y</mi><mo>−</mo><mn>25</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa113">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p245"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1695" display="inline"><mrow><mn>9</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>9</mn><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>6</mn><mi>x</mi><mo>−</mo><mn>18</mn><mi>y</mi><mo>−</mo><mn>17</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa114">
<div class="question">
<p class="para" id="fwk-redden-ch08_s06_qs01_p247"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1697" display="inline"><mrow><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>x</mi><mo>−</mo><mn>8</mn><mi>y</mi><mo>+</mo><mn>1</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd04_qd07" start="115">
<p class="para" id="fwk-redden-ch08_s06_qs01_p249"><strong class="emphasis bold">Given the graph, write the equation in general form.</strong></p>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa115">
<div class="question">
<div class="informalfigure large">
<img src="section_11/d4a159205e14de7af9b6c90a20b3d8c6.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa116">
<div class="question">
<div class="informalfigure large">
<img src="section_11/8b3405add73ee683d3abb5e71f019bfb.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa117">
<div class="question">
<div class="informalfigure large">
<img src="section_11/14e554c6a6c7ff2cc64f3d48fa25ac82.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa118">
<div class="question">
<div class="informalfigure large">
<img src="section_11/05443e5fb93d1991d3cd476acd549a2c.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa119">
<div class="question">
<div class="informalfigure large">
<img src="section_11/b84e54838134cb4347cc357008ca2d70.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa120">
<div class="question">
<div class="informalfigure large">
<img src="section_11/44368f995333d3197513a4e4a07442db.png">
</div>
</div>
</li>
</ol>
</ol>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd05">
<h3 class="title">Solving Nonlinear Systems</h3>
<ol class="qandadiv" id="fwk-redden-ch08_s06_qs01_qd05_qd01" start="121">
<p class="para" id="fwk-redden-ch08_s06_qs01_p262"><strong class="emphasis bold">Solve.</strong></p>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa121">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch08_m1705" display="block"><mrow><mrow><mo>{</mo><mtable columnspacing="0.1em"><mtr><mtd><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>8</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>−</mo><mi>y</mi><mo>=</mo><mn>4</mn></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa122">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch08_m1707" display="block"><mrow><mrow><mo>{</mo><mtable columnspacing="0.1em"><mtr><mtd><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa123">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch08_m1710" display="block"><mrow><mrow><mo>{</mo><mtable columnspacing="0.1em"><mtr><mtd><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>4</mn></mtd></mtr><mtr><mtd><mn>2</mn><mi>x</mi><mo>−</mo><mi>y</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa124">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch08_m1713" display="block"><mrow><mrow><mo>{</mo><mtable columnspacing="0.1em"><mtr><mtd><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>5</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>+</mo><mi>y</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa125">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch08_m1714" display="block"><mrow><mrow><mo>{</mo><mtable columnspacing="0.1em"><mtr><mtd><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>−</mo><mi>y</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa126">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch08_m1717" display="block"><mrow><mrow><mo>{</mo><mtable columnspacing="0.1em"><mtr><mtd><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>3</mn><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>10</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa127">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch08_m1720" display="block"><mrow><mrow><mo>{</mo><mtable columnspacing="0.1em"><mtr><mtd><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>11</mn></mtd></mtr><mtr><mtd><mn>4</mn><mi>x</mi><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>5</mn></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa128">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch08_m1723" display="block"><mrow><mrow><mo>{</mo><mtable columnspacing="0.1em"><mtr><mtd><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>y</mi><mo>=</mo><mn>5</mn></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa129">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch08_m1724" display="block"><mrow><mrow><mo>{</mo><mtable columnspacing="0.1em"><mtr><mtd><mn>5</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>10</mn></mtd></mtr><mtr><mtd><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>y</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa130">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch08_m1729" display="block"><mrow><mrow><mo>{</mo><mtable columnspacing="0.1em"><mtr><mtd><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>2</mn><mi>x</mi><mo>−</mo><mn>4</mn><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mo>−</mo><mn>3</mn></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa131">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch08_m1734" display="block"><mrow><mrow><mo>{</mo><mtable columnspacing="0.1em"><mtr><mtd><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>10</mn></mtd></mtr><mtr><mtd><mi>x</mi><mi>y</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa132">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch08_m1739" display="block"><mrow><mrow><mo>{</mo><mtable columnspacing="0.1em"><mtr><mtd><mi>y</mi><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>x</mi><mi>y</mi><mo>−</mo><mn>8</mn><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa133">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch08_m1741" display="block"><mrow><mrow><mo>{</mo><mtable columnspacing="0.1em"><mtr><mtd><mfrac><mn>1</mn><mi>x</mi></mfrac><mo>+</mo><mfrac><mn>1</mn><mi>y</mi></mfrac><mo>=</mo><mn>10</mn></mtd></mtr><mtr><mtd><mfrac><mn>1</mn><mi>x</mi></mfrac><mo>−</mo><mfrac><mn>1</mn><mi>y</mi></mfrac><mo>=</mo><mn>6</mn></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa134">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch08_m1743" display="block"><mrow><mrow><mo>{</mo><mtable columnspacing="0.1em"><mtr><mtd><mfrac><mn>1</mn><mi>x</mi></mfrac><mo>+</mo><mfrac><mn>1</mn><mi>y</mi></mfrac><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>y</mi><mo>−</mo><mi>x</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa135">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch08_m1746" display="block"><mrow><mrow><mo>{</mo><mtable columnalign="left" columnspacing="0.1em"><mtr><mtd><mi>x</mi><mo>−</mo><mn>2</mn><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>3</mn></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><msqrt><mrow><mi>x</mi><mo>−</mo><mn>4</mn></mrow></msqrt></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa136">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch08_m1748" display="block"><mrow><mrow><mo>{</mo><mtable columnspacing="0.1em"><mtr><mtd><msup><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>y</mi><mo>−</mo><msqrt><mi>x</mi></msqrt><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
</ol>
</ol>
</div>
<div class="qandaset block" id="fwk-redden-ch08_s06_qs01_ans" defaultlabel="number">
<h3 class="title">Answers</h3>
<ol class="qandadiv">
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa01_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch08_s06_qs01_p03_ans">Distance: 5 units; midpoint: <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1421" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>2</mn><mo>,</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa02_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa03_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch08_s06_qs01_p07_ans">Distance: <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1427" display="inline"><mrow><mn>4</mn><msqrt><mrow><mn>10</mn></mrow></msqrt></mrow></math></span> units; midpoint: <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1428" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>4</mn><mo>,</mo><mo>−</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa04_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa05_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch08_s06_qs01_p11_ans">Distance: <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1435" display="inline"><mrow><msqrt><mn>7</mn></msqrt></mrow></math></span> units; midpoint: <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1436" display="inline"><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><msqrt><mn>5</mn></msqrt></mrow><mn>2</mn></mfrac><mo>,</mo><mo>−</mo><mfrac><mrow><mn>7</mn><msqrt><mn>2</mn></msqrt></mrow><mn>2</mn></mfrac></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa06_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa07_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch08_s06_qs01_p16_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1443" display="inline"><mrow><mn>18</mn><mi mathvariant="italic">π</mi></mrow></math></span> square units</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa08_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa09_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch08_s06_qs01_p20_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1449" display="inline"><mrow><mfrac><mrow><mn>5</mn><mi mathvariant="italic">π</mi></mrow><mn>4</mn></mfrac></mrow></math></span> square units</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa10_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa11_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch08_s06_qs01_p25_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1454" display="inline"><mrow><mi>y</mi><mo>=</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>5</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><mn>8</mn></mrow></math></span>; vertex: <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1455" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>5</mn><mo>,</mo><mn>8</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa12_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa13_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch08_s06_qs01_p29_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1460" display="inline"><mrow><mi>y</mi><mo>=</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>−</mo><mfrac><mrow><mn>13</mn></mrow><mn>4</mn></mfrac></mrow></math></span>; vertex: <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1461" display="inline"><mrow><mrow><mo>(</mo><mrow><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>,</mo><mo>−</mo><mfrac><mrow><mn>13</mn></mrow><mn>4</mn></mfrac></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa14_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa15_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch08_s06_qs01_p33_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1466" display="inline"><mrow><mi>x</mi><mo>=</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>+</mo><mn>5</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>−</mo><mn>15</mn></mrow></math></span>; vertex: <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1467" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>15</mn><mo>,</mo><mo>−</mo><mn>5</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa16_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa17_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch08_s06_qs01_p37_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1472" display="inline"><mrow><mi>x</mi><mo>=</mo><mo>−</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>−</mo><mn>4</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><mn>13</mn></mrow></math></span>; vertex: <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1473" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>13</mn><mo>,</mo><mn>4</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa18_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa19_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch08_s06_qs01_p42_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1478" display="inline"><mrow><mi>y</mi><mo>=</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>10</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>−</mo><mn>25</mn></mrow></math></span>; </p>
<div class="informalfigure large">
<img src="section_11/897c1db754e7a1fd038af05b6edee1a5.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa20_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa21_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch08_s06_qs01_p46_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1482" display="inline"><mrow><mi>y</mi><mo>=</mo><mo>−</mo><mn>2</mn><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>−</mo><mn>6</mn></mrow></math></span>; </p>
<div class="informalfigure large">
<img src="section_11/4c5f575d96ad71dfaeaf14e720e4a33b.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa22_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa23_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch08_s06_qs01_p50_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1486" display="inline"><mrow><mi>x</mi><mo>=</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>−</mo><mn>5</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>−</mo><mn>9</mn></mrow></math></span>; </p>
<div class="informalfigure large">
<img src="section_11/e83f649f71ebd05f11d4c97a5f7992b1.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa24_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa25_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch08_s06_qs01_p54_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1490" display="inline"><mrow><mi>x</mi><mo>=</mo><mo>−</mo><mn>4</mn><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>−</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><mn>9</mn></mrow></math></span>; </p>
<div class="informalfigure large">
<img src="section_11/663ae0a27b5607cc3c234ff842fce2ad.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa26_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa27_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch08_s06_qs01_p58_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1494" display="inline"><mrow><mi>x</mi><mo>=</mo><mo>−</mo><mn>4</mn><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><mn>3</mn></mrow></math></span>; </p>
<div class="informalfigure large">
<img src="section_11/2e8569519d7b31c81ee38d7855d91e9c.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa28_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
</ol>
<ol class="qandadiv" start="29">
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa29_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch08_s06_qs01_p63_ans">Center: <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1498" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>6</mn><mo>,</mo><mn>0</mn></mrow><mo>)</mo></mrow></mrow></math></span>; radius: <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1499" display="inline"><mrow><mi>r</mi><mo>=</mo><mn>3</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa30_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa31_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch08_s06_qs01_p67_ans">Center: <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1504" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow><mo>)</mo></mrow></mrow></math></span>; radius: <span class="inlineequation"><math xml:id="fwk-redden-ch08_m1505" display="inline"><mrow><mi>r</mi><mo>=</mo><msqrt><mn>5</mn></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa32_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa33_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch08_s06_qs01_p72_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1511" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>7</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>−</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>=</mo><mn>100</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa34_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa35_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch08_s06_qs01_p76_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1517" display="inline"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>+</mo><mn>5</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>=</mo><mn>28</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa36_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa37_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch08_s06_qs01_p80_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch08_m1523" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>−</mo><mn>9</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>=</mo><mn>2</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch08_s06_qs01_qa38_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">