# Definition:Hyperbola/Focus

## Definition

Let $K$ be a hyperbola specified in terms of:

- a given straight line $D$
- a given point $F$
- a given constant $\epsilon$ such that $\epsilon > 1$

where $K$ is the locus of points $P$ such that the distance $p$ from $P$ to $D$ and the distance $q$ from $P$ to $F$ are related by the condition:

- $q = \epsilon \, p$

The point $F_1$ is known as a **focus** of the hyperbola.

The symmetrically-positioned point $F_2$ is also a **focus** of the hyperbola.

## Linguistic Note

The word **focus** is of Latin origin, hence its irregular plural form **foci**.

It was introduced into geometry by Johannes Kepler when he established his First Law of Planetary Motion. The word in Latin means **fireplace** or **hearth**, which is appropriate, considering the position of the sun.

The pronunciation of **foci** has a hard **c**, and is rendered approximately as ** folk-eye**.

Beware the solecism of pronouncing it ** fo-sigh**, which is incorrect.

## Sources

- 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $2$: The Logic of Shape: Problems for the Greeks - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**hyperbola**