Focal Property of Hyperbola

Theorem

Let $\KK$ be a hyperbola.

Let $APB$ be a tangent to $\KK$ at $P$.

Then:

$\angle APF_1 = \angle BPF_2$

where $F_1$ and $F_2$ are the foci of $\KK$.

Proof

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Also known as

The focal property of a hyperbola is also known as the reflection property.

In the context of physics, it is also called the optical property or acoustical property

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): hyperbola
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): hyperbola