Explanation Given information : The parametric equation of the curve is x = 60 t , y = 80 t -16 t 2 , and ( 0 ≤ t ≤ 3 ) , 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 = 60 t … (1) y = 80 t -16 t 2 … (2) We find the ranges of variablesx ,and y when ( 0 ≤ t ≤ 3 ) .We have ( 0 < t < 3 ) ⇒ 0 ≤ 30 t ≤ 180 ⇒ 0 ≤ x ≤ 180 … (3) ( 0 < t < 3 ) ⇒ 0 ≤ 80 t - 16 t 2 ≤ 96 ⇒ 0 ≤ y ≤ 96 … (4) Now, we eliminate the parameter between x and y as follows: From equations (1) and (2), we have x = 60 t ⇒ t = x 60 y = 80 t -16 t 2 = 80 × x 60 -16

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

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

Publisher: Kendall Hunt Publishing

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Chapter 9.5, Problem 25PS

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

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Chapter 9.5, Problem 24PS

Chapter 9.5, Problem 26PS

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Student's Solution and Survival Manual for Calculus

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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 the parameter and sketch the path described by parametric equations over the 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 the parameter and sketch the path described by parametric equations over the interval.

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