Explanation Given: Curves A and B are given as, A : x = t + t 3 , y = 3 + t 2 ; − 2 ≤ t ≤ 2 B : x = t + t 1 3 , y = 3 + t 2 3 ; a ≤ t ≤ b Calculation: The parametric equation for the curve A is A : x = t + t 3 , y = 3 + t 2 ; − 2 ≤ t ≤ 2 . Similarly, the equation of B is B : x = t + t 1 3 , y = 3 + t 2 3 ; a ≤ t ≤ b . Note that the curve B will describe the same curve as A if the time period for both curve are the same. Hence, the point on the curve A at t = − 2 must be same as the point on the curve B at t = a . Substitute t = a in x = t + t 1 3 and t = − 2 in x = t + t 3 and obtain that, a + a 1 3 = 2 + 2 3 a + a 1 3 = 2 + 8 a + a 1 3 = 10 Similarly, substitute t = a in y = 3 + t 1 3 and t = − 2 in x = 3 + t 2 3 and obtain that, 3 + a 2 3 = 3 + ( − 2 ) 2 a 2 3 = 4 a 2 = 64 a = ± 8 Therefore, a = ± 8

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Chapter 10.1, Problem 94E

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To find: The values of a and b such that the curves A and B have the same description.

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Chapter 10.1, Problem 93E

Chapter 10.1, Problem 95E

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Chapter 10 Solutions

Calculus: Early Transcendentals (2nd Edition)

Ch. 10.1 - Explain how a pair of parametric equations...Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Give parametric equations that generate the line...Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Explain how to find points on the curve x = f(t),...

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The values of a and b such that the curves A and B have the same description.

Solution Summary: The author explains that the parametric equation for the curves A and B is a=-8andb=8.

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To find: The values of a and b such that the curves A and B have the same description.

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Chapter 10 Solutions