\begin{definition}[Definition:Conic Section/Reduced Form]
Let $K$ be a conic section.
Let $K$ be embedded in a cartesian plane such that:
:$(1)$ the center is at the origin
:$(2)$ the foci are at $\left({\pm c, 0}\right)$
for some $c \in \R_{\ge 0}$.
This can be interpreted in the contexts of the specific classes of conic section as follows:
\end{definition}