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X(13), X(14), X(690), X(9180) P, P' : see below 

K451 is an axial orthopivotal cubic with orthopivot P, the intersection of the parallel at X(99) and the perpendicular at G to the Fermat line. SEARCH = 5.16053527203514. P is now X(11006) in ETC (20161123). The real asymptote contains the centers of the Jerabek and Kiepert hyperbolas. Its perpendicular at X(1649) is the axis of symmetry of the cubic. K451 is a circular cubic with singular focus F = X(1649) obviously on the axis of symmetry. X(1649) is the tripolar centroid of X(524). The reflection P' of X(99) in X(1649) lies on the cubic. It is the reflection of P about the axis of the cubic. P' = X(9180) in ETC. See also K450, K293a and K293b, three other axial orthopivotal cubics. 
