If the axis of symmetry is vertical, as it is in this case based on the vertex and focus, one of the normal forms of a parabola is (xh)^{2} = 4p(yk) where (h,k) is the vertex, and p is the distance from the vertex to the focus of the parabola.
Vertex = (1,3), Focus = (1,0), the axis of symmetry is x = 1, and p = 0(3) = +3.
So the equation of the parabola is (x(1))^{2} = 4*3*(y(3)), or
(x+1)^{2} = 12(y+3)
Note: A unique directrix is determined once you know the Vertex and Focus because it must be perpendicular to the axis of symmetry and the same distance from the vertex as the focus is.
1/13/2014

Kenneth G.