Question

Find the corresponding polar equation of the cartesian equation $(x^2+y^2{)}^2=a^2(x^2-y^2)$.

Answer 1

Given the cartesian equation is $(x^2+y^2{)}^2=a^2(x^2-y^2)$.

Let $x=r\cos \theta$ and $y=r\sin \theta$ in the above equation, then we get,

$(r^2{)}^2=a^2.r^2({\cos }^2\theta -{\sin }^2\theta )$

or, $r^2=a^2\cos 2\theta$.