Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 10.7, Problem 53HP
To determine

To write: A system of equations for hyperbola and ellipse for which a solution is (−4,8).

Expert Solution & Answer
Check Mark

Answer to Problem 53HP

The system of the equation is {x28−y264=1x264+y22563=1.

Explanation of Solution

Given:

The given solution is (−4,8).

Calculation:

Let's consider a hyperbola and an ellipse both centered in the origin as shown below.

  x2a2−y2b2=1x2c2+y2d2=1

If the system contains only terms in x2 and y2 , a solution (p,q) , in which p≠0 , q≠0 implies that (p,−q) , (−p,q) , (−p,−q) are also solutions.

So, the given system has the solutions (−4,8),(−4,−8),(4,−8),(4,8).

Substitute x=−4 and

  y=8 in the equations x2a2−y2b2=1 and x2c2+y2d2=1.

  (−4)2a2−82b2=116a2−64b2=1(−4)2c2+82d2=116c2+64d2=1

Take arbitrary values for a , c and find the values of b and d.

Take a2=8.

  168−64b2=164b2=1b2=64

Take c2=64.

  1664+64d2=164d2=3d2=2563

The system of the equations is as follows.

  x28−y264=1x264+y22563=1

Check the solutions by graph as shown below.

  Algebra 2, Chapter 10.7, Problem 53HP

Therefore, the system of the equation is {x28−y264=1x264+y22563=1.

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Chapter 10.7, Problem 52HP
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Chapter 10.7, Problem 54HP

Chapter 10 Solutions

Algebra 2

Ch. 10.1 - Prob. 1ACYPCh. 10.1 - Prob. 1BCYPCh. 10.1 - Prob. 2CYPCh. 10.1 - Prob. 3CYPCh. 10.1 - Prob. 1CYUCh. 10.1 - Prob. 2CYUCh. 10.1 - Prob. 3CYUCh. 10.1 - Prob. 4CYUCh. 10.1 - Prob. 5CYUCh. 10.1 - Prob. 6CYU
Ch. 10.1 - Prob. 7CYUCh. 10.1 - Prob. 8CYUCh. 10.1 - Prob. 9CYUCh. 10.1 - Prob. 10PPSCh. 10.1 - Prob. 11PPSCh. 10.1 - Prob. 12PPSCh. 10.1 - Prob. 13PPSCh. 10.1 - Prob. 14PPSCh. 10.1 - Prob. 15PPSCh. 10.1 - Prob. 16PPSCh. 10.1 - Prob. 17PPSCh. 10.1 - Prob. 18PPSCh. 10.1 - Prob. 19PPSCh. 10.1 - Prob. 20PPSCh. 10.1 - Prob. 21PPSCh. 10.1 - Prob. 22PPSCh. 10.1 - Prob. 23PPSCh. 10.1 - Prob. 24PPSCh. 10.1 - Prob. 25PPSCh. 10.1 - Prob. 26PPSCh. 10.1 - Prob. 27PPSCh. 10.1 - Prob. 28PPSCh. 10.1 - Prob. 29PPSCh. 10.1 - Prob. 30PPSCh. 10.1 - Prob. 31PPSCh. 10.1 - Prob. 32PPSCh. 10.1 - Prob. 33PPSCh. 10.1 - Prob. 34PPSCh. 10.1 - Prob. 35PPSCh. 10.1 - Prob. 36PPSCh. 10.1 - Prob. 37PPSCh. 10.1 - Prob. 38PPSCh. 10.1 - Prob. 39PPSCh. 10.1 - Prob. 40PPSCh. 10.1 - Prob. 41PPSCh. 10.1 - Prob. 42HPCh. 10.1 - Prob. 43HPCh. 10.1 - Prob. 44HPCh. 10.1 - Prob. 45HPCh. 10.1 - Prob. 46HPCh. 10.1 - Prob. 47STPCh. 10.1 - Prob. 48STPCh. 10.1 - Prob. 49STPCh. 10.1 - Prob. 50STPCh. 10.1 - Prob. 51SRCh. 10.1 - Prob. 52SRCh. 10.1 - 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Publisher:Wellesley-Cambridge Press
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College Algebra (Collegiate Math)
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ISBN:9780077836344
Author:Julie Miller, Donna Gerken
Publisher:McGraw-Hill Education
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