Trying to figure out how to rotate an ellipse...

Hi,

So, I have been trying to figure out how to rotate an ellipse in the form of:

My guess is that making a translate vector of T<x^2, y^2> will do the trick. My goal is simply to make the ellipse not vertical or horizontal. My reasoning is because ^2 will have moved the numbers farther away from zero more than the numbers closer to zero resulting in a rotation. Is my reasoning correct? And, how could I find the equation of an ellipse if I wanted to rotate it x degrees?