\begin{definition}[Definition:Hyperbola/Focus-Directrix]
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Let $D$ be a straight line.
Let $F_1$ be a point.
Let $e \in \R: e > 1$.
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:
:$e p = q$
Then $K$ is a '''hyperbola'''.
\end{definition}