The point of intersection of the normals to the parabola y2=4xat the ends of its latusrectum is

Any point on the parabola is (at2 , 2at) where a = 1. For the latus rectum x = a ⇒ t2  = 1⇒ t = ± 1. So ends of latus rectum are (1, ± 2). Equations of the normals at these points is given by y =– tx+2at+at3⇒x+y–3=0 and x–y–3=0 which intersect at (3, 0).