x = t^2 + 1, y = 2t + 1

Eliminating paramegter t from the two equations,

x = [(y-1)/2]^2 + 1

=> 4(x-1) = (y-1)^2

Shifting origin to (1, 1), the new coordinates (x', y') and old coordinates are related as

x' = x - 1 and y' = y - 1

=> y'^2 = 4x' is the standard equation of the parabola whose directrix is

x' = -1

=> x - 1 = -1

=> x = 0 (which is y-axis) is the directrix of the given ;parabola.