Question

Transform the polar equation to the cartesian form:

$r^2(2{\cos }^2\theta -1)=b^2$.

Answer 1

Given the equation,

$r^2(2{\cos }^2\theta -1)=b^2$

or $r^2({\cos }^2\theta -{\sin }^2\theta )=b^2$

or, $(r\cos \theta {)}^2-(r\sin \theta {)}^2=b^2$

or, $x^2-y^2=b^2$. [ Since $x=r\cos \theta$ and $y=r\sin \theta$]