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Journal for Geometry and Graphics 20 (2016), No. 1, 001--011
Copyright Heldermann Verlag 2016

The Parabola in Universal Hyperbolic Geometry. II: Canonical Points and the Y-conic

Ali Alkhaldi
Dept. of Mathematics, King Khalid University, 61431 Asir - Abha, Saudi Arabia

Norman J. Wildberger
School of Mathematics and Statistics, University of New South Wales, Sydney 2052 NSW, Australia

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 Y-conic which is homologous to the parabola, and contains many interesting meets.

Keywords: Hyperbolic geometry, projective geometry, universal geometry, hyperbolic parabola.

MSC: 51M10; 51N15, 14N99

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