SOLUTION: Write the equation for a parabola with a focus at (5,-5) and a directrix at y=-4.

Plot the focus (a point) and the directrix (a line):



The vertex is half-way between the focus and the directrix.  
Halfway between -4 (the distance the directrix is below the 
x-axis) and -5, the y-coordinate of the focus (4,-5) is the 
point (4,-4.5) or (4,-9/2).

The equation of such a parabola is 

(x-h)² =  4p(y-k)   

Where (h,k) = (4,-9/2) and |p| = the distance from the focus 
to the vertex which is also the distance from the vertex to 
the directrix. So |p| = 1/2 or 0.5.

If the parabola opens upward p is taken positive and if the 
parabola opens downward, p is taken negative.  The directrix 
is outside the parabola and the focus is inside the parabola, 
so the parabola must open downward, so p = -1/2 or -0.5

Substituting

(x-4)² = 4(-1/2)[y-(-9/2)]

(x-4)² = -2(y+9/2)    <--equation in standard form:



Edwin