Explanation Given: An equation of hyperbola y 2 − ( x + 1 ) 2 4 = 1 Approach: Compare the equation of given hyperbola with equation of shifted hyperbola, ( y − k ) 2 a 2 − ( x − h ) 2 b 2 = 1 Calculation: The shifted hyperbola has center, C(-1, 0) and It is an up-down hyperbola. Its graph will have similar shape as the unshifted hyperbola y 2 − x 2 4 = 1 (Center origin) Since a 2 = 1 and b 2 = 4 , we get a = 1 , b = 2 , and c = a 2 + b 2 = 1 + 4 = 5 = 2.236 . Thus the foci will lie 2.236 units to the up and to the down of the center, and the vertices will lie 1 unit to the up and to the down of the centre. Foci F ( − 1 , 2.236 ) and F ( − 1 , 2 To determine (b). To draw: A graph showing the hyperbola and its asymptotes.

4th Edition

ISBN: 9781305719781

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: PEARSON

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Chapter 12.4, Problem 23E

To determine

(a).

To find:

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

To determine

(b).

To draw:

A graph showing the hyperbola and its asymptotes.

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Chapter 12.4, Problem 22E

Chapter 12.4, Problem 24E

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

Solution Summary: The author compares the shifted hyperbola with the unshifted one. The center, vertices, foci, and asymptotes are similar.