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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

25-36. Graphing hyperbolas An equation of a hyperbola is given. (a) Find the center, vertices, foci, and asymptotes of the hyperbola. (b) Sketch a graph of the hyperbola.

( x 2 ) 2 8 ( y + 2 ) 2 8 = 1

To determine

a)

To find:

The center, vertices, foci, and asymptotes of the hyperbola.

Explanation

Given:

An equation (x2)28(y+2)28=1

Approach:

Using

Center=(h,k)Vertices=(±a,0)Foci=(±c,0)Asympotes y=±bax

Calculation:

Because the x2 term is positive, the hyperbola has a horizontal transverse axis.

Its vertices and foci are on the x axis.

Since a2=8 and b2=8, implies a=22, b=22, and

c=a2+b2=8+8=16=4

The equation of hyperbola having center at (h,k) is

To determine

b)

To sketch:

The graph of hyperbola.

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Chapter 12 Solutions

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