hyperbolic and elliptic involution
Given a circle and three horizontal lines a, d and f
line a cuts the circle in J and K
d and f do not cut the circle
A point A is given on line a. The polar line of A cuts line a in B.
The points A and B are in hyperbolic involution wrt J and K
Likewise points C and D, now the involution is elliptic.
The same counts for points E and F