This one question has me totally beaten. And I thought I was pretty good in co-ordinate geometry. Here it is: If the equation ax^2 + 2hxy + by^2 =1 represents an ellipse, find the square of the eccentricity of the ellipse. I know that the ratio of the distance from the directrix to the focus of a point on the ellipse is the eccentricity. But I cant figure out what the directrix is or where the foci lie. This equation must represent an ellipse with its axes shifted (as the equation with x and y axes as its major axes is (x^2/a*a) + (y*y/b*b) =1). Also, here h*h - ab <0, and abc +2fgh -af*f - bg*g -ch*h is non zero. I just dont know how to go about finding the eccentricity.