Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 10 - Parametric Equations and Polar Coordinates - 10.3 Polar Coordinates - 10.3 - Page 707: 26

Answer

$$r^2\cos 2\theta =4$$

Work Step by Step

Since $x=r\cos \theta $ and $y=r\sin \theta $ \begin{align*} x^{2}-y^{2}&=4\\ r^2\cos^2 \theta -r^2 \sin^2 \theta &=4 \\ r^2[\cos^2 \theta - \sin^2 \theta ]&=4\\ r^2\cos 2\theta&=4 \end{align*}
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