a=1 , as a=length and hence a>0,
and then your parametric equations are correct
note: as the form x=+2at , y= +at^2 is for the parabola x^2 = 4ay
and x=-2at, y=-at^2 for x^2 = -4ay(remembering that it the focal length is not making the p.eq negative)
Correct me if im wrong, but yeah