Focal Property of Conic Section
(Redirected from Reflection Property of Conic Section)
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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 $F_2$.
Focal Property of Parabola
In the case of the parabola, the focus $F_2$ is the point at infinity:
Also known as
The Focal Property of Conic Section is also known as:
- 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.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): focal property
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): focal property