Question

Convert the equation to the polar form:

$x^2-y^2=2ax$.

Answer 1

Given the equation,

$x^2-y^2=2ax$.

To convert the equation to the polar form let us put $x=r\cos \theta$ and $y=r\sin \theta$ in the above equation we get,

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

or, $r\cos 2\theta =2a\cos \theta$. [ Since $r\ne 0$]