Explanation Given: The hyperbola equation is as follows. x 2 − y 2 = 100 (1). Divide the equation (1) with the value 100 . x 2 100 − y 2 100 = 100 100 x 2 100 − y 2 100 = 1 (2). Then, compare the equation (2) with the standard equation of hyperbola, x 2 a 2 − y 2 b 2 = 1 Calculation: Compute the center of the hyperbola using the equation. ( x − h ) 2 a 2 + ( y − k ) 2 b 2 = 1 ( x − 0 ) 2 100 + ( y − 0 ) 2 100 = 1 Therefore, the center of the hyperbola ( h , k ) is ( 0 , 0 ) _ . Substitute the value 36 for a 2 and 64 for b 2 in equation (2). a 2 = 100 a = 100 a = 10 b 2 = 100 b = 100 b = 10 Compute the vertices. v e r t i c e s = ( ( h ± a ) , k ) Substitute the value 0 for h , 0 for k and 10 for a . v e r t i c e s = ( ( 0 ± 10 ) , 0 ) Then, the vertices of the hyperbola are ( ± 10 , 0 ) _ . Compute the value of c using the equation below. c 2 = a 2 + b 2 Substitute the value 10 for a and 10 for b . c 2 = ( 10 ) 2 + ( 10 ) 2 c 2 = 100 + 100 c = 200 c = 10 2 Compute the foci

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ISBN: 9781305266636

Author: James Stewart

Publisher: Cengage Learning

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Chapter 10.5, Problem 21E

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To Find: The vertices, foci and asymptotes of the hyperbola for the equation x2−y2=100.

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Chapter 10.5, Problem 20E

Chapter 10.5, Problem 22E

Chapter 10 Solutions

Single Variable Calculus

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The vertices, foci and asymptotes of the hyperbola for the equation x 2 − y 2 = 100 .

Solution Summary: The author plots the vertices, foci, and asymptotes of the hyperbola for the equation x2-y2.

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Chapter 10 Solutions