Question

Standard form equation for the parabola with the focus: F(0,4) and directrix y=3

Answer 1

a parabola is a trajectory such that the from every point on the parabola the distance to the focus and normal distance to the directrix is same

Answer 2

so here the focus is (0,4) and the directrix is y=3..
@Andy2Guns, are you here?

Answer 3

anyway, from any arbitrary point (x,y), what is the normal distance to the line y=3? obviously |y-3|
what is the distance of the point (0,4) from (x,y)? obviously
\[\sqrt{(x-0)^2+(y-4)^2}\]
so \[\sqrt{(x-0)^2+(y-4)^2}\]=|y-3|
square in both sides and solve

Answer 4

this is the equation of your required parabola