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 x:y:z = cos B - cos C:cos C - cos A:cos A - cos B meaning it has trilinear equation (cos B - cos C)/α + (cos C - cos A)/β + (cos A - cos B)/γ = 0 (Kimberling 1998, p. 237). Its center is the Feuerbach point F.

circumconic | Feuerbach's conic theorem | Jerabek hyperbola | Kiepert hyperbola | Stammler hyperbola

Karl Wilhelm Feuerbach