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A chord AB of the parabola y^2 = 12x passes through the focus S . The tangents to the parabola at A and B intersect at a point P . If both the tangents make an equal acute angle with the line 2x - y + 5 = 0 , then the value of 10 is:

Options

  1. A20
  2. B5
  3. C0
  4. D10

Correct answer

D. 10

Step-by-step solution

Since the chord AB passes through the focus S of the parabola y^2 = 12x , it is a focal chord. A known property of parabolas is that the tangents drawn at the extremities of a focal chord intersect at right angles on the directrix. Therefore, the angle between the tangent at A and the tangent at B is 90^ . We are given that both these perpendicular tangents make an equal acute angle with the line 2x - y + 5 = 0 . For a line to make equal acute angles with two mutually perpendicular lines, it must be parallel to one

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