Geodesic
The Parabola in Universal Hyperbolic Geometry. II: Canonical Points and the Y-conic
Journal for geometry and graphics, Tome 20 (2016) no. 1, pp. 1-11.

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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.
Classification : 51M10, 51N15, 14N99
Mots-clés : Hyperbolic geometry, projective geometry, universal geometry, hyperbolic parabola 
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A. Alkhaldi; N. J. Wildberger . The Parabola in Universal Hyperbolic Geometry. II: Canonical Points and the Y-conic. Journal for geometry and graphics, Tome 20 (2016) no. 1, pp. 1-11. http://geodesic.mathdoc.fr/item/JGG_2016_20_1_JGG_2016_20_1_a0/