y=−2x+12a is a normal to the parabola y2=4ax at the point whose distance from the directrixof the parabola is

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=3t  and  ATNP=3t×29t=2β.