Definition:Hyperbola/Equidistance

Definition

 * HyperbolaEquidistance.png

Let $F_1$ and $F_2$ be two points in the plane.

Let $d$ be a length less than the distance between $F_1$ and $F_2$.

Let $K$ be the locus of points $P$ which are subject to the condition:
 * $\left\lvert{d_1 - d_2}\right\rvert = d$

where:
 * $d_1$ is the distance from $P$ to $F_1$
 * $d_2$ is the distance from $P$ to $F_2$
 * $\left\lvert{d_1 - d_2}\right\rvert$ denotes the absolute value of $d_1 - d_2$.

Then $K$ is a hyperbola.

The points $F_1$ and $F_2$ are the foci of $K$.

Also see

 * Equidistance of Hyperbola equals Transverse Axis