Tilak de Alwis

Department of Mathematics, Southeastern Louisiana University, Hammond,
LA 70402, USA

FMAT1117@SELU.EDU

**Abstract**

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 the computer algebra system
*Mathematica* to illustrate and discover several aspects of these normal lines.
*Mathematica* can be used in contemporary mathematical research and education
in more than one way: as a computational, visualization, experimentation and a
conjecture forming tool. The paper well illustrates such usage via a study of the
normal lines to the ellipse. We used *Mathematica* version 3.0 on a Windows 95
platform.