Explanation Given: An equation of hyperbola ( x − 8 ) 2 − ( y + 6 ) 2 = 1 Approach: Compare the equation of given hyperbola with equation of shifted hyperbola, ( x − h ) 2 a 2 − ( y − k ) 2 b 2 = 1 Calculation: The shifted hyperbola has center, C(8,-6) and has a horizontal transverse axis. Its graph will have similar shape as the unshifted hyperbola x 2 − y 2 = 1 (Center origin) Since a 2 = 1 and b 2 = 1 , we get a = 1 , b = 1 , and c = a 2 + b 2 = 1 + 1 = 2 = 1.414 . Thus the foci will lie 1.414 units to the right and to the left of the center, and the vertices will lie 1 unit to either side of the centre. Foci F ( 9.414 , − 6 ) and F ( 6 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 22E

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 21E

Chapter 12.4, Problem 23E

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

Solution Summary: The author compares the equation of the given hyperbola with the shifted one. The center, vertices, foci, and asymptotes are the same.