Normal Lines Drawn to Ellipses and Elliptic Integrals

Tilak de Alwis
Department of Mathematics, Southeastern Louisiana University, Hammond, LA 70402, USA

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.