   Chapter 12.CT, Problem 6CT ### 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

# Find an equation for the hyperbola with foci ( 0 , ± 5 ) and with asymptotes y = ± 3 4 x .

To determine

To find:

An equation for the hyperbola with foci (0,±5) and the asymptotes y=±34x.

Explanation

Given:

The foci and asymptotes of the hyperbola are (0,±5) and y=±34x.

Approach:

From asymptotes take the value of ab and use the relation c2=a2+b2… (1)

Calculation:

Since the foci (0,±5) of the hyperbola are lying on the y-axis. Foci are equidistance from the origin and c=5. So the hyperbola must be centered at the origin and has a vertical transverse axis.

Compare y=±34x with y=±abx, we can write ab=34.

From equation (1)

c2=a2+b2

c2b2=a2

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