Possible Duplicate:
Calculating Distance of a Point from an Ellipse Border
Given a point $A = (x_1, y_1)$ and a $2$D ellipse, how could we find a point $B = (x_2, y_2)$ on the ellipse so that it has the shortest distance between point $A$ and $B$?
The point $A$ can be anywhere on the same plane of the ellipse. If possible, please list the final expression of the point $B.$