   Chapter 12.3, Problem 16E ### 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

# SKILLS9–26 Graphing Hyperbolas An equation of a hyperbola is given. (a) Find the vertices, foci, and asymptotes of the hyperbola. (b) Determine the length of the transverse axis. (c) Sketch a graph of the hyperbola. x 2 16 − y 2 12 = 1

To determine

(a)

To find:

The vertices, foci, and asymptotes of the hyperbola.

Explanation

Given:

The equation of a hyperbola is

x216y212=1.

Approach:

For a hyperbola with horizontal transverse axis

x2a2y2b2=1,a>0,b>0

The vertices are (±a,0).

The foci are (±c,0),

c2=a2+b2

The asymptotes are

y=±bax

Calculation:

The standard form of given hyperbola is

x242y2(23)2=1

Thus, a=4, b=23.

Vertices of hyperbola are (±4,0)

To determine

(b)

To find:

The length of transverse axis of the hyperbola.

To determine

(c)

To sketch:

The graph of the hyperbola.

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