(a) Explanation Definition used: Equation of a Hyperbola: Center at ( 0 , 0 ) ; Transverse axis along the x-axis: An equation of the hyperbola with the center at ( 0 , 0 ) , foci at ( − c , 0 ) and ( c , 0 ) , and vertices at ( − a , 0 ) and ( a , 0 ) is x 2 a 2 − y 2 b 2 = 1 where b 2 = c 2 − a 2 . The hyperbola has a transverse axis of length 2 a along x axis and a conjugate axis at ( 0 , ± b ) of length 2 b . “ Equation of a Hyperbola: Center at ( 0 , 0 ) ; Transverse axis along the y-axis An equation of the hyperbola with the center at ( 0 , 0 ) , foci at ( 0 , − c ) and ( 0 , c ) , and vertices at ( 0 , − a ) and ( 0 , a ) is y 2 a 2 − x 2 b 2 = 1 where b 2 = c 2 − a 2 . The hyperbola has a transverse axis of length 2 a along y axis and a conjugate axis at ( ± b , 0 ) of length 2 b (b) To determine The equation of the hyperbola for which the difference in the distances from ( − 6 , 0 ) and ( 6 , 0 ) is 8.

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

11th Edition

ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

Publisher: PEARSON+

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Chapter 21.6, Problem 45E

(a)

To determine

The equation of the hyperbola for which the difference in the distances from (−6,0) and (6,0) is 4.

(b)

To determine

The equation of the hyperbola for which the difference in the distances from (−6,0) and (6,0) is 8.

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Chapter 21.6, Problem 44E

Chapter 21.6, Problem 46E

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Chapter 21 Solutions

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

Ch. 21.1 - Find the distance between (−2, 6) and (5, −3). Ch. 21.1 - Prob. 2PE Ch. 21.1 - Prob. 1E Ch. 21.1 - Prob. 2E Ch. 21.1 - Prob. 5E Ch. 21.1 - In Exercises 5–14, find the distance between the...Ch. 21.1 - Prob. 7E Ch. 21.1 - Prob. 8E Ch. 21.1 - Prob. 9E Ch. 21.1 - Prob. 10E

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The equation of the hyperbola for which the difference in the distances from ( − 6 , 0 ) and ( 6 , 0 ) is 4.

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The equation of the hyperbola for which the difference in the distances from (−6,0) and (6,0) is 4.

The equation of the hyperbola for which the difference in the distances from (−6,0) and (6,0) is 8.

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Chapter 21 Solutions