The point of intersection of the normals to the parabola y2 = 4x  at the ends of its latus rectum is

Equation of the latus rectum is x = 1 and the coordinates of the ends of the latus rectum are (1, 2) and (1, –2). Equations of the normal at these points is y =–tx + 2at + at3 , where t = ±1, a = 1 ⇒ y + x = 3 and y – x =–3 which intersect at  (3, 0).