# Definition:Hyperbola/Equidistance

## Definition

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:

$\size {d_1 - d_2} = d$

where:

$d_1$ is the distance from $P$ to $F_1$
$d_2$ is the distance from $P$ to $F_2$
$\size {d_1 - d_2}$ 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 $K$.