JEE Mains Model Paper 25

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.