Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
4th Edition
ISBN: 9780133178579
Author: Ross L. Finney
Publisher: PEARSON
Question
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Chapter A5.2, Problem 24E
To determine

To graph: thehyperbola and explain what happens to the graph if eccentricity increases.

Expert Solution & Answer
Check Mark

Answer to Problem 24E

As the value of e increases, the slope increases.

The equation of hyperbola can now be written as: x2a2y2a2(e21)=1

Explanation of Solution

Given:

The general equation of hyperbola is x2a2y2b2=1 .

Calculation:

Therelations between c,e,a and b for the general equation of hyperbola x2a2y2a2(e21)=1

That is,

  b2=c2a2 And c=ae

This implies that,

  b2=a2e2a2    =a2(e21)

Hence the equation of hyperbola can now be written as:

  x2a2y2a2(e21)=1

The asymptotes of this hyperbola thus, have the general equation as:

  y=(±e21)x

As the value of e increases, the slope increases. If the value of e is increased to a very high value,

Then the hyperbola approaches to a single vertical line, which is the y-axis.

To draw a graph, let us assume a=1 ,and let us take various values for e=(2,3,4,5) .so we

Draw the graphs for:

  x2y23=1x2y28=1x2y215=1x2y224=1

  x2y23=1

  Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter A5.2, Problem 24E , additional homework tip  1

  x2y28=1

  Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter A5.2, Problem 24E , additional homework tip  2

  x2y215=1

  Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter A5.2, Problem 24E , additional homework tip  3

  x2y224=1

  Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter A5.2, Problem 24E , additional homework tip  4

Conclusion:

Therefore, the equation of hyperbola x2a2y2a2(e21)=1

As the value of e increases, the slope increases.

Chapter A5 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. A5.1 - Prob. 11ECh. A5.1 - Prob. 12ECh. A5.1 - Prob. 13ECh. A5.1 - Prob. 14ECh. A5.1 - Prob. 15ECh. A5.1 - Prob. 16ECh. A5.1 - Prob. 17ECh. A5.1 - Prob. 18ECh. A5.1 - Prob. 19ECh. A5.1 - Prob. 20ECh. A5.1 - Prob. 21ECh. A5.1 - Prob. 22ECh. A5.1 - Prob. 23ECh. A5.1 - Prob. 24ECh. A5.1 - Prob. 25ECh. A5.1 - Prob. 26ECh. A5.1 - Prob. 27ECh. A5.1 - Prob. 28ECh. A5.1 - Prob. 29ECh. A5.1 - Prob. 30ECh. A5.1 - Prob. 31ECh. A5.1 - Prob. 32ECh. A5.1 - Prob. 33ECh. A5.1 - Prob. 34ECh. A5.1 - Prob. 35ECh. A5.1 - Prob. 36ECh. A5.1 - Prob. 37ECh. A5.1 - Prob. 38ECh. A5.1 - Prob. 39ECh. A5.1 - Prob. 40ECh. A5.1 - Prob. 41ECh. A5.1 - Prob. 42ECh. A5.1 - Prob. 43ECh. A5.1 - Prob. 44ECh. A5.1 - Prob. 45ECh. A5.1 - Prob. 46ECh. A5.2 - Prob. 1ECh. A5.2 - Prob. 2ECh. A5.2 - Prob. 3ECh. A5.2 - Prob. 4ECh. A5.2 - Prob. 5ECh. A5.2 - Prob. 6ECh. A5.2 - Prob. 7ECh. A5.2 - Prob. 8ECh. A5.2 - Prob. 9ECh. A5.2 - Prob. 10ECh. A5.2 - Prob. 11ECh. A5.2 - Prob. 12ECh. A5.2 - Prob. 13ECh. A5.2 - Prob. 14ECh. A5.2 - Prob. 15ECh. A5.2 - Prob. 16ECh. A5.2 - Prob. 17ECh. A5.2 - Prob. 18ECh. A5.2 - Prob. 19ECh. A5.2 - Prob. 20ECh. A5.2 - Prob. 21ECh. A5.2 - Prob. 22ECh. A5.2 - Prob. 23ECh. A5.2 - Prob. 24ECh. A5.2 - Prob. 25ECh. A5.2 - Prob. 26ECh. A5.2 - Prob. 27ECh. A5.2 - Prob. 28ECh. A5.3 - Prob. 1ECh. A5.3 - Prob. 2ECh. A5.3 - Prob. 3ECh. A5.3 - Prob. 4ECh. A5.3 - Prob. 5ECh. A5.3 - Prob. 6ECh. A5.3 - Prob. 7ECh. A5.3 - Prob. 8ECh. A5.3 - Prob. 9ECh. A5.3 - Prob. 10ECh. A5.3 - Prob. 11ECh. A5.3 - Prob. 12ECh. A5.3 - Prob. 13ECh. A5.3 - Prob. 14ECh. A5.3 - Prob. 15ECh. A5.3 - Prob. 16ECh. A5.3 - Prob. 17ECh. A5.3 - Prob. 18ECh. A5.3 - Prob. 19ECh. A5.3 - Prob. 20ECh. A5.3 - Prob. 21ECh. A5.3 - Prob. 22ECh. A5.3 - Prob. 23ECh. A5.3 - Prob. 24ECh. A5.3 - Prob. 25ECh. A5.3 - Prob. 26ECh. A5.3 - Prob. 27ECh. A5.3 - Prob. 28ECh. A5.3 - Prob. 29ECh. A5.3 - Prob. 30ECh. A5.3 - Prob. 31ECh. A5.3 - Prob. 32ECh. A5.3 - Prob. 33ECh. A5.3 - Prob. 34ECh. A5.3 - Prob. 35ECh. A5.3 - Prob. 36ECh. A5.3 - Prob. 37ECh. A5.3 - Prob. 38ECh. A5.3 - Prob. 39ECh. A5.3 - Prob. 40ECh. A5.3 - Prob. 41ECh. A5.3 - Prob. 42ECh. A5.3 - Prob. 43ECh. A5.3 - Prob. 44ECh. A5.3 - Prob. 45ECh. A5.3 - Prob. 46E

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