Definition:Conic Section/Directrix

Definition

Let $K$ be a conic section specified in terms of:

a given straight line $D$
a given point $F$
a given constant $e$

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:

$q = e p$

The line $D$ is known as the directrix of the conic section.

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.