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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 10.4 - Problem 46e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 10.4 - Problem 46e

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# Solved: Equations of hyperbolas Find an equation of the

ISBN: 9780321570567 2

## Solution for problem 46E Chapter 10.4

Calculus: Early Transcendentals | 1st Edition

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Problem 46E

Problem 46E

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 (±1, 0) that passes through (, 8)

Step-by-Step Solution:

Solution 46E

Step 1:

In this problem we have to find an equation of the hyperbola with center at (0,0) with vertices  ( 1 , 0) and passing through the point (,8).

 Note; We know that a hyperbola  with the center of its origin .For these hyperbolas , the standard form of the equation is - =1 for hyperbolas that extend right and left (or)   - =1for hyperbolas that extend up and down. Consider , - =1 . In this case Center  is  ;(0,0) , vertices are ;( a, 0) ,(-a,0) , and foci is ( ae, 0) (-ae,0). Equations of the asymptotes are ; y = x , and y = x

Step 2 of 3

Step 3 of 3

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