Definition:Conic Section/Reduced Form

Definition
Let $K$ be a conic section.

Let $K$ be embedded in a cartesian coordinate 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: