How do you find the polar equation of this conic

This conic has a directrix at y = 4, an eccentricity of 1/4, and its focus is stationed at the pole (0,0).

I got r = 4/(4+sintheta)

Did you get that?

you got it right

r = ed /(1 + esin(θ))

here e = 1/4, d = 4

r = (1/4)4 /(1 + (1/4)sin(θ))

r = 1 /(4 + sin(θ))/4

r = 4/(4 + sin(θ))