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X(2), X(4), X(30), X(67), X(98), X(316), X(1352), X(4846), X(7737)

X(4846) = X(378)* isogonal conjugate of X(378)

P1 see below

The locus of the foci of all the focal cubics K(Q) of the class CL051 is K477, a focal circum-cubic with focus X(67).

It is a cubic of the same type namely K(P1) where P1 = X(7737)

The isogonal transform of K477 is K1390. See Table 73 for properties and other related cubics.

The figure below shows the locus (blue curve) of Q such that K(Q) is a focal cubic with focus F on K477. The points Q, F, P1 are collinear.