
Journal for Geometry and Graphics 20 (2016), No. 1, 001011 Copyright Heldermann Verlag 2016 The Parabola in Universal Hyperbolic Geometry. II: Canonical Points and the Yconic Ali Alkhaldi Dept. of Mathematics, King Khalid University, 61431 Asir  Abha, Saudi Arabia ahalkhaldi@kku.edu.sa Norman J. Wildberger School of Mathematics and Statistics, University of New South Wales, Sydney 2052 NSW, Australia n.wildberger@unsw.edu.au We introduce canonical points and lines for the hyperbolic parabola in Universal Hyperbolic Geometry, and explicit formulas for them in standard coordinates. Quite a few remarkable collinearities result, with the duality of the twin parabola playing a major role. We also introduce the curious Yconic which is homologous to the parabola, and contains many interesting meets. Keywords: Hyperbolic geometry, projective geometry, universal geometry, hyperbolic parabola. MSC: 51M10; 51N15, 14N99 [ Fulltextpdf (282 KB)] 