We know that $x^2+y^2+2gx+2fy+c=0$ represents a circle and the parametric solution for it is $x=\cos t, y=\sin t$.
But I was wondering what would happened for the following equation $$(xy)^2+a(xy)+bx+cy+d=0$$ where $a,b,c,d,e\in \mathbb Z.$
Can anyone help me out how to solve this equation in integers ? I have no idea on it. please show me the path.