   Chapter 12.CR, Problem 31E ### 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

# 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 + 4 ) 2 16 − y 2 16 = 1

To determine

a)

To find:

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

Explanation

Given:

An equation (x+4)216y216=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=16 and b2=16, implies a=4, b=4, and

c=a2+b2=16+16=32=42

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

To determine

b)

To sketch:

The graph of hyperbola.

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