Find a vector function that represents the curve of intersection of the two surfaces.

The cylinder x^2 + y^2 = 4 and the surface z = xy.

What I do is make z = 0, then x^2 + y^2 = 4 is a circle and

xy = 0.

Then I make these equations equal each other.

x^2 + y^2 - 4 = xy and simplify

x^2 + y^2 - xy - 4 = 0

But now I can't seem to complete the square.

Any help would be appreciated.