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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 the equation for the hyperbola that satisfies the given conditions.

Foci: ( ± 6 , 0 ) , vertices: ( ± 2 , 0 )

To determine

To find:

The equation for the hyperbola which satisfies the given conditions.

Explanation

Given:

The given conditions are,

Foci: (±6,0), Vertices: (±2,0)

Approach used:

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

(xk)2a2(yh)2b2=1 … (1)

And,

b2=c2a2 … (2)

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

The foci are given as,

(±c+h,0+k) … (3)

The vertices are given as,

(±a+h,0+k) … (4)

Calculation:

Consider the given information.

The foci are (±6,0).

Then, from equation (3),

h=0, k=0, and c=6

The vertices are (±2,0)

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