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X(2), X(3), X(6), X(13), X(14), X(397), X(398), X(37832), X(37835)

X(42610) → X(42613)

Geometric properties :

K1205 is an acnodal KHO-cubic. See K1191 for explanations and also CL075. K1198 and K1199 are two other acnodal cubics.

Its KHO-equation is : 2 x^2(y + 4z) - 9 y^2 (2y - z) = 0.

K1205 has a node at O, which is an isolated point, and a point of inflexion at K with tangent passing through X(3830).

K1205 has two other real points of inflexion with KHO-coordinates (±4√6,16,23), see orange line in the figure.

K1205 meets the Kiepert hyperbola at G (twice), X(13), X(14) and two other imaginary points (±3i√11,4,-3).

X(13), X(37835) share the same tangential (-3,8,14) and X(14), X(37832) share the same tangential (3,8,14).

The Hessian of K1205 is a similar cubic with KHO-equation : 16 x^2(13y - 2z) - 9 y^2 (y + 4z) = 0.