Focal Property of Conic Section

Theorem

Let $\KK$ be a conic section.

Let $F_1$ and $F_2$ be the foci of $\KK$.

Let $P$ be a point on $\KK$.

Let $\TT$ be the tangent to $\KK$ at $P$.

Let $\LL_1$ be the straight line through $F_1$ to $P$.

Let $\LL_2$ be the straight line through $P$ which makes the same angle with $\TT$ as does $\LL_1$.

Then $\LL_2$ passes through $F_2$.

In the case of the parabola, the focus $F_2$ is the point at infinity:

the Reflection Property of Conic Section, as it explains how light and sound are reflected by a reflector the shape of a conic section.

Hence also:

the Optical Property of Conic Section, from the way light behaves

the Acoustical Property of Conic Section, from the exploitation of the phenomenon in the science of acoustics.