(B) The minimum distance will occur along the normal to the parabola passing through (4,2) .
Normal to parabola at point Q( am2 ,−2 am) where a = 2 is y = mx − 2.2.m − 2.m3 …. (i) this normal passes through(4, 2) , hence 2 = 4m − 4m − 2m3 ⇒ m3 = −1 ⇒ m = −1. Hence point θ (2,(−1)2 ,−2∙2∙(−1)) ⇒ θ (2,4) Hence PQ=2√2