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 $$x=-\dfrac{3}{2}$$.