Given the parabola x2= -16y, what is the equation for the directrix?

Question

answers:

a) y = 4

b) y = -4

c) x = 4

d) x = -4

Answer 1

y=-x^2/16

is a parabola that passes thru(0,0) and opens downward.  It is symmetric about x=0.  The directrix is a line "behind" ( in this case above) the parabola and perpendicular to its axis of symmetry.  Among the choices, only y=4 would be possible.

This is not the analytic solution, only a selection between 4 choices.

Answer 2

x2= -16y

comparing with

x^2 = -4ay

a = 4

so the point will be (0,4)

and the equation of directrix will be y = 4