If the tangent to the curve y=x3 at the point Pt,t3 meets the curve again at Q, then the ordinate of the point which divides PQ internally in the ratio 1 : 2 is :

The equation of the tangent to the y=x3 at the point t,t3 is y−t3=3t2x−t_____1substitute y=x3 and then solve for x,yit gives x3−t3=3t2x−t⇒x−tx2+tx+t2−3t2=0⇒x−tx2+2tx−tx−2t2=0⇒x−txx+2t−tx+2t=0⇒x−t2x+2t=0Hence, Q-2t,-8t3Therefore, the ordinate of the point which divides the line segment joining P and Q in the ratio 1:2 internally is 2t3+−8t33=−2t3