The ends of the latus rectum are P(a,2a) and P′(a,2a).
Point P has parameter t1=1 and point P′ has parameter t2=1.
Normal at point P meets the curve again at point Q whose parameter t1′=−t1−t12=3
Normal at point P′ meets the curve again at point Q′ whose parameter t2′=−t2−t22=3
Hence, points Q and Q′ have coordinates (9a,6a) and (9a, 6a), respectively.
Hence, QQ′=12a.