hyperbolic parabola
parabola in the hyperbolic plane
october 2021
Poincaré disk model for the hyperbolic plane A hyperbolic LINE is the intersection of the inner of cabs () with a circle in the extended complex plane perpendicular to cabs. For two points a,b in there is an unique hyperbolic LINE through a,b. The hyperbolic distance: |a , b|hyp = | ln(|dv(a, b, s1, s2)|) |, where : complex cross-ratio, and { s1, s2 } = cabs c , c : the perpendicular circle to cabs through a,b. In the GAUSSian plane is the hyperbolic parabola a bicircular quartic, with double-point on cabs, symmetric to cabs. The directrix isn't a hyperbolic LINE! geogebra-book Brennpunkte und Leitlinien = foci & directrices hyperbolic hyperbola elliptic ellipse