Definition:Conic Section/Reduced Form/Parabola

Definition

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 if and only if:

$(1)$ its focus is at the point $\tuple {c, 0}$

$(2)$ its directrix is aligned with the line $x = -c$

for some $c \in \R_{> 0}$.