Ellipse with non-orthogonal minor and major axes? If there's an ellipse with non-orthogonal minor and major axes, what do we call it? 
For example, is the following curve a ellipse?
$x = \cos(\theta)$
$y = \sin(\theta) + \cos(\theta) $
curve $C=\vec(1,0)*\cos(\theta) + \vec(1,1)*\cos(\theta) $
The major and minor axes are $\vec(1,0)$ and $\vec(1,1)$. They are not orthogonal.
Is it still an ellipse?
Suppose I have a point $P(p_1,p_2)$ can I find a point Q on this curve that has shortest euclidean distance from P?

Hint: From $y=\sin\theta+\cos\theta$, we get $y-x=\sin\theta$, and therefore $(y-x)^2=\sin^2\theta=1-x^2$. After simplifying and completing the square, can you recognize the curve?
The major and minor axes do turn out to be orthogonal. 
