Brianchon Point

The point of Concurrence of the joins of the Vertices of a Triangle and the points of contact of a Conic Section Inscribed in the Triangle. A Conic Inscribed in a Triangle has an equation of the form

$${f\over u}+{g\over v}+{h\over w}=0,$$

so its Brianchon point has Trilinear Coordinates $(1/f, 1/g, 1/h)$. For Kiepert's Parabola, the Branchion point has Triangle Center Function

$$\alpha={1\over a(b^2-c^2)},$$

which is the Steiner Point.