Explanation Graph: Consider the parametric equations, x = 1 t − 1 …… (1) And, y = t + 1 t − 1 …… (2) Convert the above equation in the rectangular equation by elimination method as, Simplify the equation (1) as, x 2 = 1 ( t − 1 ) t − 1 = 1 x 2 t = 1 x 2 + 1 = 1 + x 2 x 2 Substitute 1 + x 2 x 2 for t in equation (2) as, y = 1 + x 2 x 2 + 1 1 + x 2 x 2 − 1 = 1 + 2 x 2 1 + x 2 − x 2 = 2 x 2 + 1 1 = 2 x 2 + 1 Thus, the required rectangular equation is y = 2 x 2 + 1 . The rectangular equation is defined for all the values of x , while the parametric equation is defined, when t − 1 > 0 , which implies that t is greater than 1 , thus, restricting the rectangular equation for positive values

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Author: Larson

Publisher: CENGAGE L

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Chapter 6.6, Problem 2ECP

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To graph: The curve represented by the equations, x=1t−1 and y=t+1t−1, by eliminating the parameters and adjusting the domain of the rectangular equation.

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Chapter 6.6, Problem 1ECP

Chapter 6.6, Problem 3ECP

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To graph: The curve represented by the equations, x = 1 t − 1 and y = t + 1 t − 1 , by eliminating the parameters and adjusting the domain of the rectangular equation.

Solution Summary: The author explains how to draw a graph of the equations by eliminating the parameters and adjusting the domain.

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To graph: The curve represented by the equations, x=1t−1 and y=t+1t−1, by eliminating the parameters and adjusting the domain of the rectangular equation.

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Chapter 6 Solutions