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X(4), X(67), X(98), X(858), X(1503)

K288 is the antigonal transform of the line HK. See also the Ehrmann strophoid K025, the Iona cubic K186 and the Canna cubic K289.

It is also the orthoassociate of the conic passing through X(4), X(25) and the vertices of the orthic triangle. See a generalization at K186.

K288 is a circular nodal cubic with node H. The nodal tangents are parallel to the asymptotes of the circum-conic passing through X(20) and X(25).

The real asymptote is the line X(112)-X(1503) parallel to the line HK. K288 meets its asymptote at X, a point on the rectangular circum-hyperbola passing through X(112).

See also CL051.

See another generalization and other related cubics in Table 43.