   Chapter 12.3, Problem 41E ### 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 the equation for the hyperbola that satisfies the given conditions.Vertices: ( ± 1 , 0 ) , asymptotes: y = ± 5 x

To determine

To find:

The equation for the hyperbola which satisfies the given conditions vertices: (±1,0), asymptotes: y=±5x.

Explanation

Given:

The given conditions are,

Vertices: (±1,0), asymptotes: y=±5x

Approach:

The general equation for a hyperbola with x axis as transverse axis is,

(xk)2a2(yh)2b2=1… (1)

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

The asymptotes are,

y=±ba(xh)+k(2)

The vertices are given as,

(±a+h,0+k) … (3)

Calculation:

Consider the given information

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