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K822

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X(54), X(523), X(1511), X(2574), X(2575)

X5-OAP points, see Table 53

K822 is a cubic that passes through the four X5-OAP points. These points lie on the stelloid K665 and on a rectangular hyperbola (H) passing through X(140), X(550) and homothetic to the Jerabek hyperbola. See also K821.

K822 meets K316 at three points on the line at infinity – namely X(523), X(2574), X(2575) – hence it has three real asymptotes. One is the perpendicular bisector of X(4)X(550) and the others are parallel to the asymptotes of the Jerabek hyperbola at X, the midpoint of X(140)X(1511).

The finite common points of K822 and K316 lie on the circum-conic (H') passing through X(30), X(54).