Convert $r^2= 9 \cos 2 \theta$ into a Cartesian equation This is how I tried so far...
$r^2= 9 \cos 2 ( \theta)$
$\cos (2 \theta) = \cos ^2 (\theta) - \sin^2 (\theta)$  and 
$r^2= x^2 + y^2$
so, it will become
$x^2 + y^2 = 9 [\cos^2 (\theta) - \sin^2 (\theta) ]$

multiply both side by $r^2$ and replace $r.cos\theta=x$ and $r.sin\theta=y$
 and  $r^2=x^2+y^2$ as $cos^2\theta-sin^2\theta=(cos\theta+sin\theta)(cos\theta-sin\theta)$
