Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

Journal for Geometry and Graphics 12 (2008), No. 2, 161--169
Copyright Heldermann Verlag 2008

Double Tangent Circles and Focal Properties of Sphero-Conics

Hans-Peter Schröcker
Unit Geometry and CAD, University Innsbruck, Technikerstr. 13, 6020 Innsbruck, Austria

We give two proofs for the characterization of a sphero-conic as locus of points such that the absolute value of the sum or difference of tangent distances to two fixed circles is constant. The first proof is based on methods of descriptive and projective geometry, the second is purely algebraic in nature. In contrast to earlier results, our proofs remain valid in case of purely imaginary tangent distances (when the sphero-conic is enclosed by both circles). Minor modifications make the algebraic proof work in the hyperbolic plane as well.

Keywords: Spherical geometry, sphero-conic, double tangent circle, focal property, elliptic geometry, hyperbolic geometry.

MSC: 51M04; 51N05, 51N25

[ Fulltext-pdf  (296  KB)] for subscribers only.