The tangent at a point P on the parabola y2 = 8x meets the directrix of the parabola at Q such that  distance of Q from the axis of the parabola is 3. Then the coordinates of P cannot be

Equation of the tangent at  P (2t2 , 4t) to the parabola is ty = x + 2t 2 which meets the directrix x =–2 of the parabola at Q for which y=2t2−2t. So that 2t2−2t=±3.⇒2t2−3t−2=0 or  2t2+3t−2=0⇒(2t+1)(t−2)=0 or  (2t−1)(t+2)=0⇒t=±2,±12So, the coordinates of P are (8,±8) or  12,±2