Explanation Given: An equation x 2 − 4 y 2 + 16 = 0 Approach: Using Center = ( h , k ) Vertices = ( 0 , ± a ) F o c i = ( 0 , ± c ) Asympotes y = ± a b x Calculation: Writing the equation in the standard form for a hyperbola x 2 − 4 y 2 + 16 = 0 x 2 − 4 y 2 = − 16 y 2 4 − x 2 16 = 1 Because the y 2 term is positive, the hyperbola has a vertical transverse axis. Its vertices and foci are on the y axis. Since a 2 = 4 and b 2 = 16 , implies a = 2 , b = 4 , and c = a 2 + b 2 = 16 + 4 = 20 = 2 5 The equation of hyperbola having center at ( h , k ) is To determine b) To sketch: The graph of hyperbola.

4th Edition

ISBN: 8220100548512

Author: Watson

Publisher: CENGAGE L

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Chapter 12.CR, Problem 30E

To determine

a)

To find:

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

To determine

b)

To sketch:

The graph of hyperbola.

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Chapter 12.CR, Problem 29E

Chapter 12.CR, Problem 31E

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Chapter 12 Solutions

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Ch. 12.1 - A parabola is the set of all points in the plane...Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - 5-10 Graphs of Parabolas Match the equation with...Ch. 12.1 - Prob. 8E Ch. 12.1 - 5-10 Graphs of Parabolas Match the equation with...Ch. 12.1 - Prob. 10E

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a) To find: The center, vertices, foci, and asymptotes of the hyperbola.

Solution Summary: The author explains how to find the center, vertices, foci, and asymptotes of the hyperbola.