A conic section $C$ (think of a parabola) has the property that, if the tangent at a point $P$ on $C$ meets the directrix $L$ at point $Q$, then the angle $\angle PFQ$, where $F$ is the focus, is a right angle. In this note the authors prove the reverse: If a curve has a point $F$ and a line $L$ such that, for every tangent at a point $P$ of $C$ that meets $L$ at $Q$, $\angle PFQ = π/2$, then $C$ is a conic section.
Reviewer: Joseph O’Rourke (Northampton)