Consider the ellipse in the standard position, and *P*, an arbitrary point on the plane. Finding the minimum distance from *P* to the ellipse is a well-known problem. One can easily show that the minimum distance path lies along a normal line to the
ellipse, passing through *P*. This paper deals with a study of all the normal lines drawn from point *P* to the ellipse. We have used *Mathematica* to illustrate and discover several aspects of these normal lines. *Mathematica* can be used in contemporary mathematical research and education as a computational, visualization, experimentation and conjecture-forming
tool. The paper well illustrates such usage via a study of the normal lines to the ellipse. We used *Mathematica* 3.0 on a Windows 95 platform.