Following [J. Geom. 108, No. 1, 45–60 (2017; Zbl 1370.51019)], the authors proceed in their investigation of a triangle \(ABC\), a point \(P\) in general position and its isotomcomplement \(Q\) (the complement of the isotomic conjugate \(P'\) of \(P\)). The focus of this article is on the conic \(C_P\) through \(A\), \(B\), \(C\), \(P\), and \(Q\).
This conic also contains the isotomic conjugate \(P'\), its isotomcomplement \(Q'\), and a couple of points derived from these points. If \(T_P\) denotes the affine map that maps \(ABC\) to the Cevian triangle of \(P\), the maps \(T_P\) and \(T_{P'}\) are conjugate in the affine group and the affine map \(\lambda := T_{P'} \circ T_P^{-1}\) fixes \(C_P\). Its unique ordinary fixed point is the center of \(C_P\) and it allows an interpretation as transformation in the Cayley-Klein model of hyperbolic geometry defined by \(C_P\).
These results (and quite a few more) are proved by synthetic reasoning alone. A forthcoming third part deals with the interpretation of the center \(Z\) of the Cevian conic \(C_p\) as generalized Feuerbach point.
For Part I, see [the authors, J. Geom. 108, No. 1, 45–60 (2017; Zbl 1370.51019)], for Part III, see [the authors, ibid. 108, No. 2, 437-455 (2017; doi:10.1007/s00022-016-0350-2)].