Finding the Shape of a Curve from the Discriminant

So apparently there's this trick to finding out the shape of a curve from the discriminant of it's equation. So let's say you have the equation that starts with 2x^2+2xy+4y^2...followed by some other stuff. Knowing that the discriminant is b^2-4ac, that gives us 2^2-4*2*4, which equals -28. Since the result is negative, the shape must be an ellipse. If it had been equal to 0, it would have been a parabola, and if it had been greater than 0, it would have been an ellipse. I don't think we learned this in class (unless I was dreaming about my girlfriend), but it's on the homework for tomorrow.