conic

A circumconic is a conic section that passes through the vertices of a triangle. Every circumconic has a trilinear equation of the form x/α + y/β + z/γ = 0 where x, y, and z are functions of the side lengths a, b, and c and x y z!=0, and conversely every circumconic has such an equation. The center of a circumconic is given by x(-a x + b y + c z):y(a x - b y + c z):z(a x + b y - c z) (Kimberling 1998, p. 235).

circumcircle | circumhyperbola | conic section | de Longchamps ellipse | Feuerbach hyperbola | Feuerbach's conic theorem | inconic | isogonal conjugate | Jerabek hyperbola | Johnson circumconic | Kiepert hyperbola | MacBeath circumconic | Steiner circumellipse