Given the points P(at2 , 2at), Q(a,0) and R (a/t2 , -2a/t) where a is a positive constant and t > 0, show that P,Q and R are collinear. Find, in terms of a and t,

(a) the area of the triangle OPR where O is the Origin.

(b) the length of PR.

Hence, deduce that the perpendicular distance from O to the line PR is 2at/1+t2.