How to find the directrix of a hyperbola

can someone explain to me how to find the directrix of a hyperbola from rectangular form? I'm completely lost. here's a sample equation, (y-2)^2 - (x^2)/4 = 1

(y - 2)^2 - x^2/4 = 1

center = (0, 2)
a = 1 , b = 2
the hyperbola has a vertical axis,
the vertices are (0, 3) and (0, 1)

the distance of the two directrices from the center is
d = a/e

where e = √(a^2 + b^2)/a
e = √(1^2 + 2^2)/1 = √5
so
d = 1/√5 = 0.4472

the directrices are then
y = 2 + 0.4472
y = 2.4472
and
y = 2 - 0.4472
y = 1.553

OG