Determine the integral of f(x,y)=xy over x^2 - xy + 2y^2 = 1 in terms of an integral over the unit circle.
The Attempt at a Solution
The associated hint is to complete the square (which I did...and got messy expressions for x and y). I would like to know how to start the problem, since changing directly to polar coordinates will not work. I have tried to use the rotation change of variables (after which I can use polar coordinates), but I do not know the angle of rotation nor the lengths of the semi- axes.
Is there another change of variables that I am overlooking?