Question

what are the vertex,focus ,directrix of 5x=(y-3)^2

Answer 1

for vertex :

we ask when is x zero
when y is 3?

so what is (x,y)??

Answer 2

you can write in a standard form

maybe the x , y zero's are easier to see

5(x-0)^2 = (y-3)^2

focus is
y^2 = 4ax but ours is y^2 =5x

so
4ax= 5x solve for a
and the y will be the same

(a,y)

the directix will be -a