distance from given point to given ellipse

Question

I have an ellipse, defined by Center Point, radiusX and radiusY, and I have a Point. I want to find the point on the ellipse that is closest to the given point. In the illustrat

Answer 1

You just need to calculate the intersection of the line [P1,P0] to your elipse which is S1.

If the line equeation is:

and the elipse equesion is:

than the values of S1 will be:

Now you just need to calculate the distance between S1 to P1 , the formula (for A,B points) is: