Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Chapter 9.3, Problem 26E
To determine

To find: The center, vertices, foci, asymptotes and graph of hyperbola x225y236=1 . Verify the result graphically.

Expert Solution & Answer
Check Mark

Answer to Problem 26E

The center of the hyperbola is (0,0) , the vertices of the hyperbola is (5,0) , (+5,0) , the foci of the hyperbola is (61,0) and (61,0) , the asymptotes of the hyperbola is y=±65x , and the graph of the hyperbola is shown in figure (1).

Explanation of Solution

Given information:

Given equation of hyperbola is x225y236=1 .

Calculation:

Compare the given equation with the standard equation of hyperbola x2a2y2b2=1 .

  a=5b=6

The center of the hyperbola is given as (0,0) .

The vertices of the hyperbola is given by (a,0) and (a,0) .

So the vertices are (5,0) and (5,0) .

The foci of the hyperbola is given by (c,0) and (c,0) , where c2=a2+b2 . Calculate the value of c .

  c2=52+62c2=25+36c2=61c=61

Hence the foci are (61,0) and (61,0) .

The asymptotes of the hyperbola is given by y=±bax .

Substitute 5 for a and 6 for b to find the asymptotes.

  y=±65x

To draw the graph of hyperbola, solve the equations of hyperbola in terms of y

  x225y236=136x225y2=90025y2=36x2900y2=36x290025

Take square root on both the sides and simplify.

  y=36x290025

Use the above equation and the asymptotes to draw the graph of the hyperbola.

. Precalculus with Limits: A Graphing Approach, Chapter 9.3, Problem 26E , additional homework tip  1

Figure (1)

Therefore, the center of the hyperbola is (0,0) , the vertices of the hyperbola is (5,0) , (+5,0) , the foci of the hyperbola is (61,0) and (61,0) , the asymptotes of the hyperbola is y=±65x and the graph of the hyperbola is shown in figure 1.

Verify the result using graphical utility:

Draw the graph for the hyperbola x225y236=1 using the graphical utility.

  Precalculus with Limits: A Graphing Approach, Chapter 9.3, Problem 26E , additional homework tip  2

From the above, it is clear that both the graphs are similar.

Hence, proved.

Chapter 9 Solutions

Precalculus with Limits: A Graphing Approach

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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. 1RECh. 9 - Prob. 2RECh. 9 - Prob. 3RECh. 9 - Prob. 4RECh. 9 - Prob. 5RECh. 9 - Prob. 6RECh. 9 - Prob. 7RECh. 9 - Prob. 8RECh. 9 - Prob. 9RECh. 9 - Prob. 10RECh. 9 - Prob. 11RECh. 9 - Prob. 12RECh. 9 - Prob. 13RECh. 9 - Prob. 14RECh. 9 - Prob. 15RECh. 9 - Prob. 16RECh. 9 - Prob. 17RECh. 9 - Prob. 18RECh. 9 - Prob. 19RECh. 9 - Prob. 20RECh. 9 - Prob. 21RECh. 9 - Prob. 22RECh. 9 - Prob. 23RECh. 9 - Prob. 24RECh. 9 - Prob. 25RECh. 9 - Prob. 26RECh. 9 - Prob. 27RECh. 9 - Prob. 28RECh. 9 - Prob. 29RECh. 9 - Prob. 30RECh. 9 - Prob. 31RECh. 9 - Prob. 32RECh. 9 - Prob. 33RECh. 9 - Prob. 34RECh. 9 - Prob. 35RECh. 9 - Prob. 36RECh. 9 - Prob. 37RECh. 9 - Prob. 38RECh. 9 - Prob. 39RECh. 9 - Prob. 40RECh. 9 - Prob. 41RECh. 9 - Prob. 42RECh. 9 - Prob. 43RECh. 9 - Prob. 44RECh. 9 - Prob. 45RECh. 9 - Prob. 46RECh. 9 - Prob. 47RECh. 9 - Prob. 48RECh. 9 - Prob. 49RECh. 9 - Prob. 50RECh. 9 - Prob. 51RECh. 9 - Prob. 52RECh. 9 - Prob. 53RECh. 9 - Prob. 54RECh. 9 - Prob. 55RECh. 9 - Prob. 56RECh. 9 - Prob. 57RECh. 9 - Prob. 58RECh. 9 - Prob. 59RECh. 9 - Prob. 60RECh. 9 - Prob. 61RECh. 9 - Prob. 62RECh. 9 - Prob. 63RECh. 9 - Prob. 64RECh. 9 - Prob. 65RECh. 9 - Prob. 66RECh. 9 - Prob. 67RECh. 9 - Prob. 68RECh. 9 - Prob. 69RECh. 9 - Prob. 70RECh. 9 - Prob. 71RECh. 9 - Prob. 72RECh. 9 - Prob. 73RECh. 9 - Prob. 74RECh. 9 - Prob. 75RECh. 9 - Prob. 76RECh. 9 - Prob. 77RECh. 9 - Prob. 78RECh. 9 - Prob. 79RECh. 9 - Prob. 80RECh. 9 - Prob. 81RECh. 9 - Prob. 82RECh. 9 - Prob. 83RECh. 9 - Prob. 84RECh. 9 - Prob. 85RECh. 9 - Prob. 86RECh. 9 - Prob. 87RECh. 9 - Prob. 88RECh. 9 - Prob. 89RECh. 9 - Prob. 90RECh. 9 - Prob. 91RECh. 9 - Prob. 92RECh. 9 - Prob. 93RECh. 9 - Prob. 94RECh. 9 - Prob. 95RECh. 9 - Prob. 96RECh. 9 - Prob. 97RECh. 9 - Prob. 98RECh. 9 - Prob. 99RECh. 9 - Prob. 100RECh. 9 - Prob. 101RECh. 9 - Prob. 102RECh. 9 - Prob. 103RECh. 9 - Prob. 104RECh. 9 - Prob. 105RECh. 9 - Prob. 106RECh. 9 - Prob. 107RECh. 9 - Prob. 108RECh. 9 - Prob. 109RECh. 9 - Prob. 110RECh. 9 - Prob. 111RECh. 9 - Prob. 112RECh. 9 - Prob. 113RECh. 9 - Prob. 114RECh. 9 - Prob. 115RECh. 9 - Prob. 116RECh. 9 - Prob. 117RECh. 9 - Prob. 118RECh. 9 - Prob. 119RECh. 9 - Prob. 120RECh. 9 - Prob. 121RECh. 9 - Prob. 122RECh. 9 - Prob. 123RECh. 9 - Prob. 124RECh. 9 - Prob. 125RECh. 9 - Prob. 126RECh. 9 - Prob. 127RECh. 9 - Prob. 128RECh. 9 - Prob. 129RECh. 9 - Prob. 130RECh. 9 - Prob. 131RECh. 9 - Prob. 132RECh. 9 - Prob. 133RECh. 9 - Prob. 134RECh. 9 - Prob. 135RECh. 9 - Prob. 136RECh. 9 - Prob. 137RECh. 9 - Prob. 138RECh. 9 - Prob. 139RECh. 9 - Prob. 140RECh. 9 - Prob. 141RECh. 9 - Prob. 142RECh. 9 - Prob. 143RECh. 9 - Prob. 144RECh. 9 - Prob. 145RECh. 9 - Prob. 146RECh. 9 - Prob. 147RECh. 9 - Prob. 148RECh. 9 - Prob. 149RECh. 9 - Prob. 150RECh. 9 - Prob. 151RECh. 9 - Prob. 152RECh. 9 - Prob. 153RECh. 9 - Prob. 154RECh. 9 - Prob. 155RECh. 9 - Prob. 156RECh. 9 - Prob. 157RECh. 9 - Prob. 158RECh. 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. 1CLTCh. 9 - Prob. 2CLTCh. 9 - Prob. 3CLTCh. 9 - Prob. 4CLTCh. 9 - Prob. 5CLTCh. 9 - Prob. 6CLTCh. 9 - Prob. 7CLTCh. 9 - Prob. 8CLTCh. 9 - Prob. 9CLTCh. 9 - Prob. 10CLTCh. 9 - Prob. 11CLTCh. 9 - Prob. 12CLTCh. 9 - Prob. 13CLTCh. 9 - Prob. 14CLTCh. 9 - Prob. 15CLTCh. 9 - Prob. 16CLTCh. 9 - Prob. 17CLTCh. 9 - Prob. 18CLTCh. 9 - Prob. 19CLTCh. 9 - Prob. 20CLTCh. 9 - Prob. 21CLTCh. 9 - Prob. 22CLTCh. 9 - Prob. 23CLTCh. 9 - Prob. 24CLTCh. 9 - Prob. 25CLTCh. 9 - Prob. 26CLTCh. 9 - Prob. 27CLTCh. 9 - Prob. 28CLTCh. 9 - Prob. 29CLTCh. 9 - Prob. 30CLTCh. 9 - Prob. 31CLTCh. 9 - Prob. 32CLTCh. 9 - Prob. 33CLTCh. 9 - Prob. 34CLTCh. 9 - Prob. 35CLTCh. 9 - Prob. 36CLTCh. 9 - Prob. 37CLTCh. 9 - Prob. 38CLTCh. 9 - Prob. 39CLTCh. 9 - Prob. 40CLTCh. 9 - Prob. 41CLTCh. 9 - Prob. 42CLTCh. 9 - Prob. 43CLTCh. 9 - Prob. 44CLTCh. 9 - Prob. 45CLTCh. 9 - Prob. 46CLTCh. 9 - Prob. 47CLTCh. 9 - Prob. 48CLTCh. 9 - Prob. 49CLTCh. 9 - Prob. 50CLTCh. 9 - Prob. 51CLTCh. 9 - Prob. 52CLTCh. 9 - Prob. 53CLTCh. 9 - Prob. 54CLTCh. 9 - Prob. 55CLT
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