write the equation of a parabola with focus (0,4) and directrix y=-4

Some books give the standard form of a y-parabola as

(1)                    y = a(x - h)² + k

and others give this as its standard form.

(2)             (x - h)² = 4p(y - k)

It doesn't matter which your book uses.  They are equivalent if a = 1/(4p)

The vertex of a parabola is the point halfway between the focus and the
directrix.  The point halfway between the focus (0,4) and the horizontal
directrix y=-4 is the origin (0,0), so if your book uses (1), then it is of
the form 

(3)                    y = ax² 

If your book uses (2), then it is of the form:

(4)                   x² = 4py

p represents the distance from the vertex to the focus, which is considered a
positive number if the directrix is below the vertex and focus, and negative
number if the directrix is above the vertex and focus.

In this case p = +4, so a = 1/(4(4)) or 1/16

If your book uses form (1), then the answer is 

(5)                    y = (1/16)x²    


If your book uses form (2), then the answer is x² = 4(4)y or

(6)                   x² = 16y


Edwin
AnlytcPhil@aol.com