PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Question
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Chapter 9, Problem 42CR

a.

To determine

To find: The standard form of the equation of hyperbola

a.

Expert Solution
Check Mark

Answer to Problem 42CR

The standard form of the equation of hyperbola is (y+3)24(x+1)225=1

Explanation of Solution

Given information:

The given expression is 4x2+25y28x+150y+121=0

Calculation:

By completing the square, write the original equation in standard form

  4x2+25y28x+150y+121=0  [Original equation]25(y2+6y)4(x2+2x)=121  [Group terms and factor 4 and 25 out of x and y terms]25(y2+6x+9)4(x2+2x+1)=121++2254  [Complete the squares]25(y+3)24(x+1)2=100  [Write in completed square form](y+3)24(x+1)225=1  [Standard form]

Therefore, the standard form of the equation of hyperbola is (y+3)24(x+1)225=1

b.

To determine

To find: The center, vertices, foci and asymptotes of the hyperbola

b.

Expert Solution
Check Mark

Answer to Problem 42CR

The center, vertices, foci and asymptotes of the hyperbola are (1,3) , [(1,1),(1,5)] , (1,3±29) and 292

Explanation of Solution

Given information:

The given expression is 4x2+25y28x+150y+121=0

The standard form of the equation of hyperbola is (y+3)24(x+1)225=1

Determine the value of a and b from the obtained standard equation of hyperbola

  a=2 and b=5

The transverse axis is vertical where, h=1, k=3, a=2, b=5 and c is obtained as,

  c=a2+b2c=22+52c=4+25c=29

The center, vertices, foci and asymptote of the hyperbola can be obtained as,

The center of the hyperbola is (h,k)=(1,3)

The vertices of the hyperbola is (h,k±a)=(1,1),(1,5)

The foci of the hyperbola is (h,k±c)=(1,3±29)

The eccentricity (e)=ca=292

Therefore, the center, vertices, foci and asymptotes of the hyperbola are (1,3) , [(1,1),(1,5)] , (1,3±29) and 292

c.

To determine

To graph: The equation of hyperbola

c.

Expert Solution
Check Mark

Explanation of Solution

Given information:

The given expression is 4x2+25y28x+150y+121=0

Graph:

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 9, Problem 42CR

Interpretation: The equation is plotted and the graph is obtained

Chapter 9 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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Prob. 47ECh. 9.7 - Prob. 48ECh. 9.7 - Prob. 49ECh. 9.7 - Prob. 50ECh. 9.7 - Prob. 51ECh. 9.7 - Prob. 52ECh. 9.7 - Prob. 53ECh. 9.7 - Prob. 54ECh. 9.7 - Prob. 55ECh. 9.7 - Prob. 56ECh. 9.7 - Prob. 57ECh. 9.7 - Prob. 58ECh. 9.7 - Prob. 59ECh. 9.7 - Prob. 60ECh. 9.7 - Prob. 61ECh. 9.7 - Prob. 62ECh. 9.7 - Prob. 63ECh. 9.7 - Prob. 64ECh. 9.7 - Prob. 65ECh. 9.7 - Prob. 66ECh. 9.7 - Prob. 67ECh. 9.7 - Prob. 68ECh. 9.7 - Prob. 69ECh. 9.7 - Prob. 70ECh. 9.7 - Prob. 71ECh. 9.7 - Prob. 72ECh. 9.7 - Prob. 73ECh. 9.7 - Prob. 74ECh. 9.7 - Prob. 75ECh. 9.7 - Prob. 76ECh. 9.7 - Prob. 77ECh. 9.7 - Prob. 78ECh. 9.7 - Prob. 79ECh. 9.7 - Prob. 80ECh. 9.7 - Prob. 81ECh. 9.7 - Prob. 82ECh. 9.7 - Prob. 83ECh. 9 - Prob. 1CRCh. 9 - Prob. 2CRCh. 9 - Prob. 3CRCh. 9 - Prob. 4CRCh. 9 - Prob. 5CRCh. 9 - Prob. 6CRCh. 9 - Prob. 7CRCh. 9 - Prob. 8CRCh. 9 - Prob. 9CRCh. 9 - Prob. 10CRCh. 9 - Prob. 11CRCh. 9 - Prob. 12CRCh. 9 - Prob. 13CRCh. 9 - Prob. 14CRCh. 9 - Prob. 15CRCh. 9 - Prob. 16CRCh. 9 - Prob. 17CRCh. 9 - Prob. 18CRCh. 9 - Prob. 19CRCh. 9 - Prob. 20CRCh. 9 - Prob. 21CRCh. 9 - Prob. 22CRCh. 9 - Prob. 23CRCh. 9 - Prob. 24CRCh. 9 - Prob. 25CRCh. 9 - Prob. 26CRCh. 9 - Prob. 27CRCh. 9 - Prob. 28CRCh. 9 - Prob. 29CRCh. 9 - Prob. 30CRCh. 9 - Prob. 31CRCh. 9 - Prob. 32CRCh. 9 - Prob. 33CRCh. 9 - Prob. 34CRCh. 9 - Prob. 35CRCh. 9 - Prob. 36CRCh. 9 - Prob. 37CRCh. 9 - Prob. 38CRCh. 9 - Prob. 39CRCh. 9 - Prob. 40CRCh. 9 - Prob. 41CRCh. 9 - Prob. 42CRCh. 9 - Prob. 43CRCh. 9 - Prob. 44CRCh. 9 - Prob. 45CRCh. 9 - Prob. 46CRCh. 9 - Prob. 47CRCh. 9 - Prob. 48CRCh. 9 - Prob. 49CRCh. 9 - Prob. 50CRCh. 9 - Prob. 51CRCh. 9 - Prob. 52CRCh. 9 - Prob. 53CRCh. 9 - Prob. 54CRCh. 9 - Prob. 55CRCh. 9 - Prob. 56CRCh. 9 - Prob. 57CRCh. 9 - Prob. 58CRCh. 9 - Prob. 59CRCh. 9 - Prob. 60CRCh. 9 - Prob. 61CRCh. 9 - Prob. 62CRCh. 9 - Prob. 63CRCh. 9 - Prob. 64CRCh. 9 - Prob. 65CRCh. 9 - Prob. 66CRCh. 9 - Prob. 67CRCh. 9 - Prob. 68CRCh. 9 - Prob. 69CRCh. 9 - Prob. 70CRCh. 9 - Prob. 71CRCh. 9 - Prob. 72CRCh. 9 - Prob. 73CRCh. 9 - Prob. 74CRCh. 9 - Prob. 75CRCh. 9 - Prob. 76CRCh. 9 - Prob. 77CRCh. 9 - Prob. 78CRCh. 9 - Prob. 79CRCh. 9 - Prob. 80CRCh. 9 - Prob. 81CRCh. 9 - Prob. 82CRCh. 9 - Prob. 83CRCh. 9 - Prob. 84CRCh. 9 - Prob. 85CRCh. 9 - Prob. 86CRCh. 9 - Prob. 87CRCh. 9 - Prob. 88CRCh. 9 - Prob. 89CRCh. 9 - Prob. 90CRCh. 9 - Prob. 91CRCh. 9 - Prob. 92CRCh. 9 - Prob. 93CRCh. 9 - Prob. 94CRCh. 9 - Prob. 95CRCh. 9 - Prob. 96CRCh. 9 - Prob. 97CRCh. 9 - Prob. 98CRCh. 9 - Prob. 99CRCh. 9 - Prob. 100CRCh. 9 - Prob. 101CRCh. 9 - Prob. 102CRCh. 9 - Prob. 103CRCh. 9 - Prob. 104CRCh. 9 - Prob. 105CRCh. 9 - Prob. 106CRCh. 9 - Prob. 107CRCh. 9 - Prob. 1CTCh. 9 - Prob. 2CTCh. 9 - Prob. 3CTCh. 9 - Prob. 4CTCh. 9 - Prob. 5CTCh. 9 - Prob. 6CTCh. 9 - Prob. 7CTCh. 9 - Prob. 8CTCh. 9 - Prob. 9CTCh. 9 - Prob. 10CTCh. 9 - Prob. 11CTCh. 9 - Prob. 12CTCh. 9 - Prob. 13CTCh. 9 - Prob. 14CTCh. 9 - Prob. 15CTCh. 9 - Prob. 16CTCh. 9 - Prob. 17CTCh. 9 - Prob. 18CTCh. 9 - Prob. 19CTCh. 9 - Prob. 20CTCh. 9 - Prob. 21CTCh. 9 - Prob. 22CTCh. 9 - Prob. 23CTCh. 9 - Prob. 24CTCh. 9 - Prob. 25CTCh. 9 - Prob. 1STPCh. 9 - Prob. 2STPCh. 9 - Prob. 3STPCh. 9 - Prob. 4STPCh. 9 - Prob. 5STPCh. 9 - Prob. 6STPCh. 9 - Prob. 7STPCh. 9 - Prob. 8STPCh. 9 - Prob. 9STPCh. 9 - Prob. 10STPCh. 9 - Prob. 11STPCh. 9 - Prob. 12STPCh. 9 - Prob. 13STPCh. 9 - Prob. 14STPCh. 9 - Prob. 15STPCh. 9 - Prob. 16STPCh. 9 - Prob. 17STPCh. 9 - Prob. 18STPCh. 9 - Prob. 19STPCh. 9 - Prob. 20STPCh. 9 - Prob. 21STPCh. 9 - Prob. 22STPCh. 9 - Prob. 23STPCh. 9 - Prob. 24STPCh. 9 - Prob. 25STPCh. 9 - Prob. 26STPCh. 9 - Prob. 27STP
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