Answer
$$ y =\frac{6}{x^2}$$
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.
$$ y =\frac{6}{x^2}$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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
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