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 - 12.3 Polar Coordinates - Exercises - Page 619: 40



Work Step by Step

Since $r^2=\cos (2\theta)$, then we have $$r^2=\cos^2\theta-\sin^2\theta=\frac{x^2}{r^2}-\frac{y^2}{r^2}.$$ Hence, $r^4=x^2-y^2$, which can be written in the form $$(x^2+y^2)^2=x^2-y^2.$$
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