Note: This is a homework problem.
I'm trying to show that conic section $ax^2 + 2bxy + cy^2 = d$ is an ellipse or the empty set if $ac-b^2\gt 0$. There are others to show but if I can understand this one, I should be able to get them without too much trouble.
Unfortunately I don't have much to show for what I've tried as I haven't gotten far enough into any ideas. In fact, I'm quite stuck as to how I can even start. It seems to be related to the descriminant but I'm not sure how.
Thank you very much for any help, I've been staring at this for most of the day.