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: 11


$$ y =\frac{6}{x^2}$$

Work Step by Step

Given $$ x=e^{-2t},\ \ \ \ y= 6e^{4t}$$ Since $ e^{2t}=\frac{1}{x}$, then \begin{align*} y&= 6e^{4t}\\ &= 6(e^{2t})^2\\ &=\frac{6}{x^2} \end{align*} i.e. $$ y =\frac{6}{x^2}$$
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