Electronic Proceedings
of the 12th Asian Technology Conference in Mathematics
Abstract
for 12982
Locii Associated with Tangents and Normals
of Conic Sections
Authors: Tilak dealwis
Affiliations: Southeastern Louisiana University
Keywords: Intermediate, Undergraduate Level
In this paper, we will investigate several locus problems associated
with tangent lines and normal lines of conic sections. The conic
sections we consider include parabolas and ellipses, but hyperbolas
will be left to the reader. For example, given an arbitrary point P
on one of these conic sections, consider the tangent line and/or the
normal line to the conic at that point. One can form several regions
bounded by these tangent lines, normal lines, other auxiliary lines,
and the conic section itself. We are primarily interested in
investigating the locus of the center of gravity of these regions as
the point P moves along the conic section. The computer algebra
system Mathematica was used to help with our computations.