Circumhyperbola
A circumhyperbola is a circumconic that is a hyperbola. A rectangular circumhyperbola always passes through the orthocenter H and has center on the nine-point circle, a result known as the Feuerbach's conic theorem. The following table summarizes a number of rectangular circumhyperbolas, together with their centers and most important fifth incident point. rectangular circumhyperbola | Kimberling | center | Kimberling | incident point(s) Feuerbach hyperbola | X_11 | Feuerbach point F | X_1, X_7, X_8, X_9 | incenter, Gergonne point, Nagel point, mittenpunkt Jerabek hyperbola | X_125 | | X_3, X_6 | circumcenter, symmedian point Kiepert hyperbola | X_115 | | X_2, X_10, X_13, X_14 | triangle centroid, Spieker center, first Fermat point, second Fermat point | X_137 | | X_5 | nine-point center