Focal Property of Ellipse

Theorem

Let $\EE$ be an ellipse.

Let $P$ be an arbitrary point on $\EE$.

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

Then:

$\angle APF_1 = \angle BPF_2$

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

Proof

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Also known as

The focal property of an ellipse 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): ellipse
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): ellipse