Efficient algorithm needed

[Brian K. W. Hook]

I am working on a Windows 3.0 version of XEYES and need a very fast and not
necessarily accurate algorithm for determining the following:

Given an ellipse and a point, determine where a line from the center of the
ellipse to the point will intersect the ellipse.

You are give:

The center of the ellipse
The width of ellipse
The height of the ellipse
The X and Y coordinate of the point

I need efficiency mostly, since I will be running this on Windows (which is
strapped for resources as is) and I am doing this calculation 10 times per
second.

Brian

PS Please email replies if possible.