   Chapter 12.3, Problem 51E ### 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

# Perpendicular Asymptotes(a) Show that the asymptotes of the hyperbola x 2 − y 2 = 5 are perpendicular to each other.(b) Find an equation for the hyperbola with foci ( ± c , 0 ) and with asymptotes perpendicular to each other.

To determine

(a)

To show:

The asymptotes of the hyperbola x2y2=5 are perpendicular to each other.

Explanation

Approach:

The equation of the pair of asymptotes of hyperbola x2y2=a2 is given by,

x2y2=0

The condition for two lines to be perpendicular is,

m1m2=1

Here, m1 and m2 are slope of lines.

Calculation:

Consider the given equation.

x2y2=5

The equation of the pair of asymptotes is,

x2y2=0(x+y)(xy)=0

To determine

(b)

To find:

The equation for the hyperbola with foci (±c,0) and with asymptotes perpendicular to reach other.

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