Construction of a conic from the 5 points P0 ... P4.
Construct Q3, Q'3, Q4, Q'4, V.
Now let there be an arbitrary line, p, through P1. Q is the point where the line p
meets p2, then Q' is the point where VQ meets p1. Now, P is the point where P2Q'
meets P1Q. The locus of points P as p rotates is the conic through the 5 given
points.
In this Cinderella construction, the points P0 ... P4 are free. The light blue conic
is the locus of point P as the orange line l rotates.
This is the construction of Colin Maclaurin (1698-1746), as described in "Introduction
to Projective Geometry" by C. R. Wylie, Jr. (Dover, 2008).
-- David Bakin
