#### Answer

$$(x^2+y^2)^2=x^2-y^2.$$

#### 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
$$(x^2+y^2)^2=x^2-y^2.$$

Published by
W. H. Freeman

ISBN 10:
1464125260

ISBN 13:
978-1-46412-526-3

$$(x^2+y^2)^2=x^2-y^2.$$

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