The equation of a parabola with vertex (h,k) with horizontal axis is
(y-k)² = 4p (x-h) , where |p| is the distance of the focus (or directrix) from the vertex.
1/2 Latus rectum = Distance from the directrix to the focus. (verify using the definition of parabola)
Since the vertex lies in the middle of the directrix and focus, |p| = 3.
Therefore the equation of the parabola is
(y-2)² = 4(±3) (x-1)
(y-2)² = ±12 (x-1)
Note: The sign indicates where the parabola opens. In this case, if it's +, then it opens to the right. Otherwise, it opens to the left.