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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

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.

Vertices ( 0 , ± 6 ) , hyperbola passes through ( 5 , 9 )

To determine

To find:

The equation for the hyperbola with vertices (0,±6), and the it passes through (5,9).

Explanation

Given:

The vertices are (0,±6), and the hyperbola passes through (5,9).

Approach:

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

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

b2=c2a2...(2)

The length of the transverse axis is

l=2a ...(3)

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

Calculation:

Since the vertices are (0,±6).

Use the midpoint formula to find h and k.

(h,k)=(0+02,662)=(0,0)

So, h=0, k=0

From the equation (3), the length of the transverse axis is

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