I presume that, by "latus rectum as 2", you mean that the length of the latus rectum is 2. In a parabola that is always 4 times the distance from the vertex to the focus so that distance is 1/2. that is also the distance from the vertex to the directrix so the vertex must be at (-1+ 1/2, 1)= (-1/2, 1) (with the parabola opening in the positive x direction) or at (-1- 1/2, 1)= (-3/2, 1) (with the parabola opening in the negative x direction).