centers of the Apollonius circles
The circular line passes through X(351), X(523) : any point on this line has a circular polar conic :
– that of X(351) – the center of the Parry circle and also the tripolar centroid of X(6) – degenerates into the line at infinity and the radical axis of the pencil of circles passing through X(187), X(524), X(2482),
– that of X(523) is the Parry circle.
The orthic line is the tangent at X(110) to the circumcircle : any point on this line has a polar conic which is a rectangular hyperbola. These rectangular hyperbolas form a pencil having the same infinite points – that of the rectangular circum-hyperbola through X(110) – and two other common finite points lying on the radical axis above.
K604 is a nK0+ with three concurring asymptotes at X(351) but only one is real. See K150 for other cubics nK0+.