A circumconic hyperbola, which therefore passes through the orthocenter, is a rectangular hyperbola, and has center on the nine-point circle. Its circumconic parameters are given by
 |
meaning it has trilinear equation
 |
(Kimberling 1998, p. 237).
Its center is the Feuerbach point 
(Kimberling 1998, p. 237).
It passes through the vertices of a triangle and Kimberling centers 
for 
(incenter),
4 (orthocenter), 7 (Gergonne point), 8 (Nagel point), 9 (mittenpunkt), 21 (Schiffler point), 79, 80, 84, 90, 104, 177, 256, 294, 314, 885, 941, 943, 981, 983, 987, 989, 1000, 1039, 1041, 1061, 1063, 1156, 1172, 1251, 1320, 1389, 1392, 1476, 1896, 1937, 2298, 2320, 2335, 2344, 2346, 2481, 2648, and 2997.
The Feuerbach hyperbola is the isogonal conjugate of the line 
,
where 
is the circumcenter and 
is the incenter of 
.
