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This page is about Focus of Hyperbola. For other uses, see focus.



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 foke-eye.

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