The correct option is C (−16,−14)
Let the point P be (2t1,2t1)
Slope of the normal through P is t21⋯(1)
Let the normal at P meet again at Q(2t2,2t2)
Slope of the normal at QP=2/t2−2/t12t2−2t1=−1t1t2⋯(2)
From (1) and (2),
t31.t2=−1
Given point is P(1,4)
⇒t1=1/2;t2=−8
Thus Q will be (−16,−14)