# 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.

### Eccentricity

The constant $\epsilon$ is known as the **eccentricity** of the ellipse.

## Also see

## Historical Note

The focus-directrix definition of a conic section was first documented by Pappus of Alexandria.

It appears in his *Collection*.

As he was scrupulous in documenting his sources, and he gives none for this construction, it can be supposed that it originated with him.