You are given an ellipse in parametric form
$ E(t) = C + E_1 \cos(t) + E_2 \sin(t) $
where $C$, $E_1$, $E_2$ are $2-$ or $3-$ dimensional vectors corresponding to an ellipse specified in two dimensions or three dimensions, respectively. In addition, you're given a point $P_0$, and you want to find points $A$ and $B$ on the ellipse that are a minimum/maximum distance away from $P$
The context is finding the distance between any point in the plane and an ellipse, just as you would find the distance between a point and a line or a point and a plane.