5L-s-Co1: 5L-Inscribed Conic

It is well known that in a system of 5 random lines a unique inscribed conic can be constructed.
5L s Co1 Inscribed Conic 01

See Ref-19.
1. Given five lines a, b, c, d, e.
2. Let A0 = cd, B0 = de, C0 = ea, D0 = ab, E0 = bc.
3. The line from A0 through B0D0.C0E0 cuts a in A on the conic, and so on cyclically.
4. We now have five points A, B, C, D, E on the curve.
5. Now go further with construction 5P-s-Co1.

5L-s-P1 is the center of this conic.