Explanation Given information : The parametric equation of the curve is x =1+si n 2 t , y =- 2 + cos t , and ( 0 ≤ t ≤ π ) , Formula used : We eliminate parameter from the parametric equations x = f 1 ( t ) , y = f 2 ( t ) , and sketch the graph in x - y plane. Calculations: The parametric form of the curve is x =1+si n 2 t .............(1) y =- 2 + cos t .............(2) We find the ranges of variablesx ,and y when ( 0 ≤ t ≤ π ) .We have ( 0 ≤ t ≤ π ) ⇒ 0 ≤ 1+si n 2 t ≤ 2 ⇒ 0 ≤ x ≤ 0 ( y -axis) .............(3) ( 0 < t < π ) ⇒ -1 ≤ -2+cos t ≤ -3 ⇒ -1 ≤ y ≤ -3 .............(4) Now, we eliminate the parameter between x and y as follows: From equations (1), and (2), we have si n 2 t = x -1 y =- 2 + cos t ⇒ cos t = ( y + 2 ) ⇒ cos 2 t = ( y + 2 ) 2 Now, si n 2 t + cos 2 t = ( x -1 ) + ( y + 2 ) 2

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 9.5, Problem 32PS

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Tofind:An explicit relationship between x and y from the equations x=f1(t) , y=f2(t) by elimination of the parameter and sketch the path described by parametric equations over the given interval.

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Chapter 9.5, Problem 31PS

Chapter 9.5, Problem 33PS

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Tofind: An explicit relationship between x and y from the equations x = f 1 ( t ) , y = f 2 ( t ) by elimination of the parameter and sketch the path described by parametric equations over the given interval.

Solution Summary: The author calculates the parametric form of the curve by eliminating the parameter and sketching the graph in x-y plane.

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Tofind:An explicit relationship between x and y from the equations x=f1(t) , y=f2(t) by elimination of the parameter and sketch the path described by parametric equations over the given interval.

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