Explanation Given: The function is x 2 n + 1 + y 2 n + 1 = a x n y n . Calculation: The function is x 2 n + 1 + y 2 n + 1 = a x n y n . … (1) Define one of the variable from x or y to be the parameter t . Let y = t x . Substitute t x for y in the equation (1). x 2 n + 1 + ( t x ) 2 n + 1 = a x n ( t x ) n x 2 n + 1 ( 1 + t 2 n + 1 ) = a t n x 2 n x 2 n + 1 ( 1 + t 2 n + 1 ) − a t n x 2 n = 0 Take x 2 n as common. x 2 n ( ( 1 + t 2 n + 1 ) x − a t n ) = 0 That is, x 2 n = 0 or ( ( 1 + t 2 n + 1 ) x − a t n ) = 0 x = 0 or x = a t n 1 + t 2 n + 1 Now, take x = y t . Substitute y t for x in the equation (1)...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 12.1, Problem 82E

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Find a parametrization of $x^{2 n + 1} + y^{2 n + 1} = a x^{n} y^{n}$ , where a and n are constants.

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Chapter 12.1, Problem 81E

Chapter 12.1, Problem 83E

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Chapter 12 Solutions

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Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 7PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

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Find a parametrization of x 2 n + 1 + y 2 n + 1 = a x n y n , where a and n are constants.

Solution Summary: The author explains how to determine the parametrization of x = a t n + 1 + y 2 = 1.

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Find a parametrization of $x^{2 n + 1} + y^{2 n + 1} = a x^{n} y^{n}$ , where a and n are constants.

Want to see the full answer?

Chapter 12 Solutions

Find a parametrization of x 2 n + 1 + y 2 n + 1 = a x n y n , where a and n are constants.

Solution Summary: The author explains how to determine the parametrization of x = a t n + 1 + y 2 = 1.

Concept explainers

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Find a parametrization of x2n+1+y2n+1=axnyn, where a and n are constants.

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Chapter 12 Solutions

Find a parametrization of $x^{2 n + 1} + y^{2 n + 1} = a x^{n} y^{n}$ , where a and n are constants.