Originally Posted by

**s_ingram** Hi folks,

I was looking at the following equation:

$2x^2 + 3y^2 -4xy + 2x -6y + 3 = 0$

I put it into a graphing tool and it looks like an ellipse. But is it an ellipse? I am saying it isn't because it has the 'xy' term in it.

So my question is: how do I know what a shape is? The eye is not a precise instrument, so a thing can look like a circle and not be. My equation looks like an ellipse, but I'm guessing it isn't.

So there are lots of shapes that look like ellipses and hyperbolas, but may not be. So what do we call these shapes?

Any comments on this would be appreciated.