Definition:Hyperbola/Focus

Definition

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

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.

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.