Parametric equations of an ellipse in an arbitrary plane at an arbitrary orientation?

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I have searched both on here and on stackoverflow for answers to this question and I can't seem to find a good answer relating to what I'm doing.

I have a center point and two vectors, one that is in the minor axis direction with minor radius length and one that is in the major axis direction with major radius length. From this, I need to be able to generate points along the path of an ellipse of arbitrary orientation in an arbitrary plane. Can I define an ellipse using just these three things? And how?

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This should give you an ellipse around point P with axis vectors $\mathbf{u}$ and $\mathbf{v}$ $$\mathbf{r} = P + \mathbf{u} \cos(t) + \mathbf{v} \sin(t)$$