16 5. The point P (ap2, 2ap), where a is a positive constant, lies on the parabola with equation y2 = 4ax The normal to the parabola at P meets the parabola again at the point Q (aq2, 2aq) (a) Show that q p p = − − 2 2 (5) (b) Hence show that PQ ka p p n 2 2 4 2 1 = + ( ) where k and n are integers to be determined. (5) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________