Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.1 Parametric Equations - Exercises - Page 603: 12


$$ y =(1-x)^{-2}$$

Work Step by Step

Given $$ x=1+t^{-1},\ \ \ \ y= t^2$$ Since $ t=\frac{1}{x-1}$, then \begin{align*} y&= t^2\\ &= \frac{1}{(x-1)^2}\\ &=(1-x)^{-2} \end{align*} i.e. $$ y =(1-x)^{-2}$$
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