# Polar form of elliptic curve?

My instructor asked us to find the polar form of the elliptic curve defined by the equation $$y^2=x^3+ax+b$$

What I did:

Using $$x=r\cos\theta$$ and $$y=r\sin\theta$$, I got

$$r^2\sin^2\theta=r^3\cos^3\theta+ar\cos\theta+b$$

That's all I got so far. I want to derive an equation of $$r$$ in terms of $$\theta$$, so I'm not sure how to advance from this.

Any help will be greatly appreciated.

You can solve the cubic equation in $$r$$ by means of the Cardano formula, after depression. Nothing really nice. In fact, plain awful.