
Journal for Geometry and Graphics 12 (2008), No. 2, 161169 Copyright Heldermann Verlag 2008 Double Tangent Circles and Focal Properties of SpheroConics HansPeter Schröcker Unit Geometry and CAD, University Innsbruck, Technikerstr. 13, 6020 Innsbruck, Austria hanspeter.schroecker@uibk.ac.at We give two proofs for the characterization of a spheroconic 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 spheroconic is enclosed by both circles). Minor modifications make the algebraic proof work in the hyperbolic plane as well. Keywords: Spherical geometry, spheroconic, double tangent circle, focal property, elliptic geometry, hyperbolic geometry. MSC: 51M04; 51N05, 51N25 [ Fulltextpdf (296 KB)] for subscribers only. 