Originally Posted by

**Stonehambey** The problem is to prove that the following curve is an ellipse

$\displaystyle r=\frac{2a}{3+2\cos\theta}$

I've looked about and have found the equation of the ellipse in polar form, but I can't find it's derivation or proof anywhere.

Anyway, I started this problem by subbing in

$\displaystyle r = \sqrt{x^2+y^2}$

and

$\displaystyle x = r\cos\theta$

But I ended up with a horrible mess and couldn't spot how to get it into the form $\displaystyle \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$