Let the equation of the parabola be y2 = 4ax and P (at12 , 2at1) , Q (at22 , 2at2) be the extremities ofthe chord PQ. The coordinates of T, the point of intersection of the tangents at P and Q are (at1t2 , a(t1+t2)) Now SP = a(1+t12) SQ = a(1+t22) And ST2 = (at1t2−a)2 + [a(t1+t2)−0]2 = a2(t12+t22+t12t22+1) = a2(1+t12)(1+t22) = SP. SQ So that SP, ST, SQ are in G.P.