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JEE Math Practice Question

Let P : y2 = 4ax, a > 0 be a parabola with focus S. Let the tangents to the parabola P make an angle of $${\pi \over 4}$$ with the line y = 3x + 5 touch the parabola P at A and B. Then the value of a for which A, B and S are collinear is :

  1. A.8 only
  2. B.2 only
  3. C.$${1 \over 4}$$ only
  4. D.any a > 0

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