PN is an ordinate of the parabola y2=9x .A straightline is drawn through the mid-point M of PN parallelto the axis of the parabola meeting the parabolaat Q. NQ meets the tangent at the vertex A, at apoint T, then AT/NP =

Let P be 9t2/4,9t/2 then NP=9t/2.MN=9t/4equation of MQ is y=9t/4 which meets the parabolay2=9x at the point Q9t2/16,9t/4,N is 9t2/4,0equation of NQ is y=−9×164×27tx−94t2 which meets the tangentx=0 (at the vertex A) at the point for whichy=3t so that AT=3t1 and  ATNP=3t×29t=23.