Reduced equation of the vertical parabola

Let's consider the vertical parabola, where the vertex is in the origin and the parabola lies on the $x$ axis.

The focus is now at point $F(0,\dfrac{p}{2})$, and the equation of the generator line $D$ is: $y=-\dfrac{p}{2}$.

The equation of the parabola is $$x^2=2py$$

Considering the equation $x^2=12y$, find its focus, its generator line and its vertex.

The vertex is, by definition, at $A(0,0)$.

Comparing $x^2=12y$ with $x^2=2py$ we can see that $2p=12$ and therefore $p=6$.

Substituting $p$, we can find the focus $F(0,3)$ and the generator line $y=-3$.