Reduced equation of the horizontal parabola

Let's consider the parabola which vertex coincides with the origin and which axis coincides with the $x$-axis.

In this case, the focus is at point $F(\dfrac{p}{2},0)$, and the equation of the generator line $D$ is: $x=-\dfrac{p}{2}$.

The equation of the parabola is $$y^2=2px$$

Considering the equation $y^2=-6x$, find its vertex, its focus and its generator line.

By definition, in this type of equations the vertex is $A(0,0)$.

We can identify $y^2=-6x$ with $y^2=2px$ and obtain $2p=-6$ and $p=-3$.

Therefore, the focus is at $F(\dfrac{p}{2},0)$, which is at $F(-\dfrac{3}{2},0)$.

To substitute $p$ in $x=-\dfrac{p}{2}$.

The equation of the generator line is $x=-\dfrac{3}{2}$.