convert equation from polar coordinate to cartesian coordinate

Question

I have the following equation $$r= \frac{A}{\log\left[B\tan\left(\frac{\theta}{2N}\right)\right]}$$

For using an optimization program, I would like to have this equation in cartesian coordinate system. Is it possible to have x,y equations for the above equation.

Answer 1

Implicitly possible as:

$$ Exp {\dfrac { A }{ \sqrt {x^2 + y^2} } } = B \, tan \,[ \dfrac { \tan^{-1} \frac{y}{x} } {2 N } ] $$