Answer
$r^{2}\cos 2\theta=1$
Work Step by Step
Conversion formulas: $\left\{\begin{array}{ll}
(x,y)=(r\cos\theta,r\sin\theta) & \\
r^{2}=x^{2}+y^{2}, & \tan\theta=\frac{y}{x}
\end{array}\right.$
$ x^{2}\rightarrow r^{2}\cos^{2}\theta$
$ y^{2}\rightarrow r^{2}\sin^{2}\theta$
Rewrite the equation in terms of $r$ and $\theta$.
$r^{2}\cos^{2}\theta-r^{2}\sin^{2}\theta=1$
$r^{2}(\cos^{2}\theta-\sin^{2}\theta)=1\qquad $
(recognize the double angle identity.)
$r^{2}\cos 2\theta=1$
