parametrics parabola wise is simple.
you just differentiate x^2=4ay
therefore y=X^2/4a
dy/dx = x/2a
sub in x = (say 2ap or 2am cause x=2at)
then you get dy/dx = m or p or what ever
(normal = -1/(m or p or what ever)
then do the old y-y1 = m(x-x1) to find the tangent/normal
or if your given points, just find the point and sub into x^2=4ay
theres not often many other questions than that