The angle between tangents to the parabola y^2 = 4ax at the points where it intersects with the line x – y – a = 0 is

Q: The angle between tangents to the parabola y2 = 4ax at the points where it intersects with the line x – y – a = 0 is

(A) π/3

(B) π/4

(C) π/6

(D) π/2

Sol. The coordinates of the focus of the parabola y2 = 4ax are (a, 0). The line x – y – a = 0 passes through this point.

Therefore it is a focal chord of the parabola. Hence the tangents intersect at right angle.

Hence (D) is the correct answer.