Definition:Hyperbola/Focus-Directrix

Definition

 * HyperbolaFocusDirectrix.png

Let $D$ be a straight line.

Let $F$ be a point.

Let $\epsilon \in \R: \epsilon > 1$.

Let $K$ be 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:


 * $\epsilon \, p = q$

Then $K$ is a hyperbola.

Directrix
The line $D$ is known as the directrix of the hyperbola.

Focus
The point $F$ is known as the focus of the hyperbola.

Also see

 * Equivalence of Definitions of Hyperbola