Definition:Parabola/Focus-Directrix

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Definition

ParabolaFocusDirectrix.png


Let $D$ be a straight line.

Let $F$ be a point.


Let $K$ be the locus of points $P$ such that the distance $p$ from $P$ to $D$ equals the distance $q$ from $P$ to $F$:

$p = q$


Then $K$ is a parabola.


Directrix

The line $D$ is known as the directrix of the parabola.


Focus

The point $F$ is known as the focus of the parabola.


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.


Sources