Question 370136
x = 3 is the equation of a vertical line. A parabola with a vertical line directrix will be a parabola that opens horizontally (to the right or to the left).<br>
Since the focus, (-3, 0), is to the left of the directrix, this parabola will open to the left (so that the focus is inside the "bowl" of the parabola).<br>
A parabols that opens to the left will have an equation of the form:
{{{-4p(x-h) = (y-k)^2}}}
The squaring of y is what makes the parabola open horizontally, 
The minus in front of 4p makes it open to the left. (A positive would makeit open to the right.)<br>
The h and k in the equation are the coordinates of the vertex. The vertex is halfway between the focus and the directrix, The point which is halfway between (-3, 0) and the line x = 3 would be (0, 0). So the vertex is (0, 0) which makes h = k = 0.<br>
The "p" in the equation is the distance between the focus and directrix. The distance from the focus, (-3, 0), and the vertex, (0, 0), is 3. So p = 3.<br>
Replacing the h, k and p into
{{{-4p(x-h) = (y-k)^2}}}
we get:
{{{-4(3)(x-(0)) = (y-(0))^2}}}
which simplifies as follows:
{{{-4(3)(x) = (y)^2}}}
{{{-12x = y^2}}}