Definition:Hyperbola/Focus-Directrix

Definition

 * HyperbolaFocusDirectrix.png

Let $D$ be a straight line.

Let $F_1$ be a point.

Let $\epsilon \in \R: \epsilon > 1$.

Let $K$ be the locus of points $P$ such that the distance $p$ from $P$ to $D$ and the distance $q$ from $P$ to $F_1$ are related by the condition:


 * $\epsilon \, p = q$

Then $K$ is a hyperbola.

Also see

 * Equivalence of Definitions of Hyperbola


 * Hyperbola has Two Foci


 * Definition:Circle
 * Definition:Ellipse
 * Definition:Parabola