### The conic ABCPP^{•} and the affine mapping T_{P}

Conic C_{P} passing through the five points ABCPQ, where ABC
is a given ordinary triangle and Q=cP^{•} is the isotomcomplement of P, defined
as the complement of the isotomic conjugate P^{•} of P with respect to triangle
ABC.

The map T_{P} is the affine map which takes
triangle ABC to the cevian triangle DEF of P with respect to ABC.

The map T_{P•} is the affine map which takes
triangle ABC to the cevian triangle D'E'F' of P^{•} with respect to ABC.

cP^{•} is a fixed point of T_{P}, cP is a fixed point of T_{P•} and Z (center of the conic C_{P}) is a fixed point of
T_{P•} _{º} T_{P}^{-1}.

**
The conic C**_{P} is parabola if and only if P lies on the Tucker nodal cubic (K015).

The conic C_{P} is rectangular hyperbola if and only if P lies on the Lucas cubic (K007).

http://amontes.webs.ull.es/otrashtm/HGT2016.htm

Angel Montesdeoca. Octubre, 2016