Directrix at y=3,axis x=2 Latus rectum 4

Answer 1

assuming you mean a parabola,

recall that x^2 = 4py has
axis x=0
directrix at y = -p
latus rectum = 4p

So, your equation is

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

see

http://www.wolframalpha.com/input/?i=parabola+(x-2)%5E2+%3D+4(y-4)