Definition:Parabola/Focus-Directrix
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Definition
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
- Results about parabolas can be found here.
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
- 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text {IV}$. The Ellipse: $1 \text a$. Focal properties
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): parabola