\begin{definition}[Definition:Hyperbola/Equidistance]
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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 $K$.
\end{definition}