\begin{definition}[Definition:Conic Section/Reduced Form/Parabola]
Let $K$ be a parabola embedded in a cartesian plane.
As a Parabola has no Center, it is not possible to define the reduced form of a parabola in the same way as for the other classes of conic section.
Instead, $K$ is in '''reduced form''' {{iff}}:
:$(1)$ its focus is at the point $\tuple {c, 0}$
:$(2)$ its directrix is aligned with the line $x = -c$
for some $c \in \R_{> 0}$.
:400px
Category:Definitions/Parabolas
\end{definition}