- #1

chaoseverlasting

- 1,050

- 3

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 can't 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 don't know how to go about finding the eccentricity.