Equations of hyperbolas Find an equation of the following

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

ISBN: 9780321570567 2

Solution for problem 45E Chapter 10.4

Calculus: Early Transcendentals | 1st Edition

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Problem 45E

Equations of hyperbolas Find an equation of the following hyperbolas, assuming the center is at the origin. Sketch a graph labeling the vertices, foci, and asymptotes. Use a graphing utility to check your work.

A hyperbola with vertices (±4, 0) and foci (±6, 0)

Step-by-Step Solution:

Solution 45E

Step 1:

In this problem we have to find an equation of the hyperbola with center at (0 ,0) with vertices ( $\frac{+}{\ }$ 4 , 0) and foci ( $\frac{+}{\ }$ 6 , 0).

Note; We know that a hyperbola with the center of its origin .For these hyperbolas , the standard form of the equation is ${\frac{{x}^{2}}{{a}^{2}}}^{\ }$ - $\frac{{y}^{2}}{{b}^{2}}$ =1 for hyperbolas that extend right and left (or)

$\frac{{y}^{2}}{{b}^{2}}$ - ${\frac{{x}^{2}}{{a}^{2}}}^{\ }$ =1for hyperbolas that extend up and down.

Consider , ${\frac{{x}^{2}}{{a}^{2}}}^{\ }$ - $\frac{{y}^{2}}{{b}^{2}}$ =1 . In this case ${b}^{2}={a}^{2}(1-{e}^{2})\ ,\ here\ e\ >\ 1.$

Center is ;(0,0) , vertices are ;( a, 0) ,(-a,0) , and foci is ( ae, 0) (-ae,0).

Equations of the asymptotes are ; y = $\frac{b}{a}$ x , and y = $\frac{-b}{a}$ x

Step 2 of 3

Chapter 10.4, Problem 45E is Solved

Step 3 of 3

Textbook: Calculus: Early Transcendentals

Edition: 1

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

ISBN: 9780321570567

The answer to “Equations of hyperbolas Find an equation of the following hyperbolas, assuming the center is at the origin. Sketch a graph labeling the vertices, foci, and asymptotes. Use a graphing utility to check your work.A hyperbola with vertices (±4, 0) and foci (±6, 0)” is broken down into a number of easy to follow steps, and 43 words. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. This full solution covers the following key subjects: foci, vertices, Hyperbolas, graphing, equation. This expansive textbook survival guide covers 112 chapters, and 5248 solutions. Since the solution to 45E from 10.4 chapter was answered, more than 329 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 45E from chapter: 10.4 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM.