Question 1059942
3y^2=24x


{{{3y^2=24x}}}
{{{3(y-0)^2=24(x-0)}}}


That is the form which might be arranged if deriving the equation from parabola of known focus and known directrix.  Vertex would be  (0,0).  Axis of Symmetry would be {{{y=0}}}.


You want one further adjustment to YOUR equation.
{{{(1/3)3(y-0)^2=(1/3)24(x-0)}}}

{{{(y-0)^2=8(x-0)}}}--------conforming to the format  {{{(y-k)^2=4p(x-h)}}}.


The meaning of p is the distance of the vertex from either directrix or focus.  Notice here that p is a POSITIVE value.


{{{4p=8}}}
{{{p=2}}}
-
This means the focus is  (0,2) and the directrix is {{{x=-2}}}.



See here for helpful lessons on using Distance Formula for the Definition of Parabola to derive equation:


<a href="https://www.youtube.com/watch?v=M8LGsQMwwj4">Use definition to derive parabola equations.</a>


<a href="https://www.youtube.com/watch?v=Wworlx39KfQ">Same idea, different orientation</a>