If the normals at the end points of a variable chord PQ of the parabola y^2 – 4y – 2x = 0 are perpendicular,

Q: If the normals at the end points of a variable chord PQ of the parabola y2 – 4y – 2x = 0 are perpendicular, then the tangents at P and Q will intersect at

(A) x + y = 3

(B) 3x – 7 = 0

(C) y+3 = 0

(D) 2x + 5 = 0

Sol. Since normals at P and Q are perpendicular, the tangents at P and Q will also be perpendicular but any two perpendicular tangents of a parabola always intersect on its directrix.

The parabola is (y – 2)2 = 2(x + 2).

So its directrix is 2x + 5 = 0

Hence (D) is the correct answer.