   Chapter 12.CR, Problem 36E ### 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. y 2 = x 2 + 6 y

To determine

a)

To find:

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

Explanation

Given:

An equation y2=x2+6y

Approach:

Using

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

Calculation:

Writing the equation in the standard form for a hyperbola

y2=x2+6yy26y+99x2=0(y3)2x2=9(y3)29(x0)29=1

Because the y2 term is positive, the hyperbola has a vertical transverse axis.

Its vertices and foci are on the y axis.

Since a2=9 and b2=9, implies a=3, b=3, and

c=a2+b2=9+9=18=32

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

To determine

b)

To sketch:

The graph of hyperbola.

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