Explanation Given: The equation of the hyperbola is: y 2 9 − x 2 16 = 1 Approach: If the hyperbola equation is y 2 a 2 − x 2 b 2 = 1 then the vertices, foci and asymptotes can be calculated as formula: Vertex: ( 0 , a ) and ( 0 , − a ) Foci: ( 0 , c ) and ( 0 , − c ) , where c = a 2 + b 2 Asymptotes: y = a b x and y = − a b x Calculation: Compare the following two equations: y 2 a 2 − x 2 b 2 = 1 y 2 9 − x 2 16 = 1 The obtained value of a is 3 and b is 4 , so vertices are ( 0 , 3 ) , ( 0 , − 3 ) To determine (b) To find: The length of transverse axis, To determine (c) To plot: The graph of equation y 2 9 − x 2 16 = 1 .

4th Edition

ISBN: 9781305719781

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: PEARSON

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Chapter 12.3, Problem 10E

To determine

(a)

To find:

The vertex, foci, and asymptotes on the hyperbola.

To determine

(b)

To find:

The length of transverse axis,

To determine

(c)

To plot:

The graph of equation y29−x216=1.

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Chapter 12.3, Problem 9E

Chapter 12.3, Problem 11E

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Chapter 12 Solutions

Algebra and Trigonometry

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 vertex, foci, and asymptotes on the hyperbola.

Solution Summary: The author compares the equations of the hyperbola: vertices, foci, and asymptotes.

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(a) To find: The vertex, foci, and asymptotes on the hyperbola.

(b) To find: The length of transverse axis,

(c) To plot: The graph of equation y29−x216=1.

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Chapter 12 Solutions

(a)

To find:

The vertex, foci, and asymptotes on the hyperbola.

(b)

To find:

The length of transverse axis,

(c)

To plot:

The graph of equation y29−x216=1.