The vertex is always halfway between the focus and the directrix, and the parabola always curves away from the directrix.
so if the focus is at (0,2) and the directrix is at y = 4
the vertex would be halfway between here
So the vertex, exactly between the focus and directrix, must be at (h, k) = (0, 1). The absolute value of p is the distance between the vertex and the focus and the distance between the vertex and the directrix. (The sign on p tells me which way the parabola faces.) Since the focus and directrix are six units apart, then this distance has to be
three units, so  p  = 3.
now to determine the direction the parbola is going to curve it is going to curve away from the directix which is a line at 4 parallel to the x axis
since the vertex is at (0,1) the parabola will curve down which tells me this is a regular parabola so the eqn is
(x – h)^{2} = 4p(y – k)
we know h,k and p (p is = p because it is pointing down
(x0)^{2} = 4(3)(y1)
x^{2} = 12(y1)
now if your directix was parallel to the y axis you would have used the formula
(x – h)2 = 4p(y – k)
9/24/2013

Felice R.