(a) Explanation Given: The given hyperbola is x 2 − 2 y 2 = 16 . Definition used: Definition: 1: “The equation of the hyperbola is x 2 a 2 − y 2 b 2 = 1 , where c = a 2 + b 2 , a > 0 , b > 0 with center at the origin, vertices ( − a , 0 ) , ( a , 0 ) and foci F 1 ( − c , 0 ) , F 2 ( c , 0 ) ”. Definition -2: “The equation of the asymptotes of the hyperbola x 2 a 2 − y 2 b 2 = 1 are x a + y b = 0 and x a − y b = 0 ”. The equation of hyperbola is x 2 − 2 y 2 = 16 . Simplify, the above equation as follows, x 2 16 − 2 y 2 16 = 1 x 2 16 − y 2 8 = 1 Compare the equation x 2 16 − y 2 8 = 1 with the hyperbola x 2 a 2 − y 2 b 2 = 1 . a 2 = 16 ( Take positive square root both sides ) a = 4 And b 2 = 8 ( Take positive square root both sides ) b = 2 2 Clearly, a = 4 , b = 2 2 and a > 0 , b > 0 (b) To determine To sketch: The graph of the hyperbola x 2 − 2 y 2 = 16 .

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Author: Stewart

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Chapter 11, Problem 29RE

(a)

To determine

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

(b)

To determine

To sketch: The graph of the hyperbola x2−2y2=16.

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Chapter 11, Problem 28RE

Chapter 11, Problem 30RE

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Chapter 11 Solutions

PRECALCULUS: MATHEMATICS FOR CALCULUS

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

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

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

To sketch: The graph of the hyperbola x2−2y2=16.

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Chapter 11 Solutions