Braikenridge-Maclaurin Construction

The converse of Pascal's Theorem. Let $A_1$, $B_2$, $C_1$, $A_2$, and $B_1$ be the five points on a Conic. Then the Conic is the Locus of the point

$$C_2=A_1(z\cdot C_1A_2)\cdot B_1(z\cdot C_1B_2),$$

where $z$ is a line through the point $A_1B_2\cdot B_1A_2$.

See also Pascal's Theorem