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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

SKILLS

9–26 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.

9 x 2 4 y 2 = 36

To determine

(a)

To find:

The vertices, foci, and asymptotes of the hyperbola.

Explanation

Given:

The equation of a hyperbola is

9x24y2=36

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 obtained as follows.

9x24y2=369x2364y236=1x24y29=1x222y232=1

This gives, a=2, b=3

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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