   Chapter 12.3, Problem 45E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# 37-50 Finding the equation of a Hyperbola Find an equation for the hyperbola that satisfies the given conditions.Asymptotes y = ± x , hyperbola passes through ( 5 , 3 ) .

To determine

To find:

The equation of the hyperbola with the asymptotes y=±x, and it passes through (5,3).

Explanation

Approach:

The general equation of a hyperbola with x-axis as the transverse axis is given by

(xh)2a2(yk)2b2=1...(1)

And b2=c2a2...(2)

The asymptotes are given by,

y=±ab(xh)+k...(3)

Here, a is the transverse axis, b is the conjugate axis, c is the focus, and (h,k) is the center of the hyperbola.

Calculation:

Compare y=±x with the equation (3), we get

h=0, k=0,

ab=±1

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