Definition:Ellipse/Focus-Directrix

Definition


Let $D$ be a straight line.

Let $F$ be a point.

Let $\epsilon \in \R: 0 < \epsilon < 1$.

Let $K$ be the locus of points $b$ 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 an ellipse.

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

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

Also see

 * Equivalence of Definitions of Ellipse


 * Ellipse has Two Foci