Convert $r^2\cos(2\theta)=9$ to Cartesian

Question

I need to convert $r^2\cos(2\theta)=9$ to Cartesian coordinates.
How should I do it?
What I did: $$r^{2}\cos2\theta=r^{2}2\cos^{2}\theta-1=9\Rightarrow r^{2}\cos^{2}\theta=5\Rightarrow x^{2}=5$$ Did I'm right?
Thank you!!

Answer 1

$$r^2 \cos (2\theta ) =r^2 \cos^2 \theta -r^2 \sin^2 \theta $$ but $$x=r\cos \theta , y=r\sin\theta $$ so we obtain $$x^2 -y^2 =9.$$