[SOLVED] Conversion of Polar and Rectangular Equations

I need to convert this rectangular equation into polar form:

$\displaystyle x^4 + 2x^2y^2 + y^4 = 2xy$

I know that $\displaystyle x = rcos\theta$ and $\displaystyle y = rsin\theta$. I've tried a little substitution but have not had a lot of success in simplifying it.

I also need to convert this polar equation into rectangular form:

$\displaystyle r^2 = \frac{36}{9cos^2\theta - 4sin^2\theta}$

I have a suspicion that $\displaystyle r^2 = x^2 + y^2$ is a useful tool, but I am having trouble with the conversion still. I used it to create this simplified equation in rectangular form:

$\displaystyle y = \frac{6}{3cos\theta - 2sin\theta} -x$ Is this right? I simply substituted $\displaystyle r^2$, subtracted $\displaystyle x^2$ and took the square root of everything. Is this correct?