   Chapter 10, Problem 51RE

Chapter
Section
Textbook Problem

Find an equation of the hyperbola with foci (0, ±4) and asymptotes y = ±3x.

To determine

To find: The equation of the hyperbola with foci (0,±4) and asymptotic equation y=±3x .

Explanation

Given:

The foci of the hyperbola are at (0,±4) .

Asymptotes of the hyperbola are of equation y=±3x .

Calculation:

The foci of the hyperbola are at (0,±c) .

Asymptotes of the hyperbola are of the equation y=abx .

Write the distance of the foci from the origin c as below.

c=4

Use the equation for hyperbola as below.

a2+b2=c2

Substitute 3b for a and 4 for c .

(3b)2+b2=429b2+b2=16b2=1610

b2=85

Slope of the Asymptotes of the hyperbola is as below.

ab=3

Simplify the above equation.

a=3ba2=(3b)2a2=9b2

Substitute 85 for b2 in the above equation

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