OK so I did a little more work, and figure I should times both sides by r instead of squaring it.

which gave me:

r^2= r + rsin(t)

x^2+y^2=r+y

r= (x^2+y^2-y)

r^2= (x^2+y^2-y)^2

x^2+y^2= (x^2+y^2-y)^2

But I'm still stuck on how to find the derivative of this? [dy/dx] = [dy/dt / dx/dt ]