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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

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 16 y 2 = 1

To determine

(a)

To find:

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

Explanation

Given:

The equation is given as,

9x216y2=1

Approach:

The equation of a hyperbola with center (0,0) and horizontal transverse axis is, x2a2y2b2=1(1)

The coordinates of the vertices are (±a,0). … (2)

The coordinates of the foci are (±c,0). … (3)

Here, c=a2+b2(4)

The asymptotes are y=±bax(5)

Calculation:

Consider the equation of the hyperbola.

9x216y2=1x2(13)2y2(14)2=1

This implies that a=13, b=14

Substitute 13 for a, and 14 for b in equation (4).

To determine

(b)

To find:

The length of the transverse axis.

To determine

(c)

To sketch:

The graph of the hyperbola.

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