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Let P: y^(2) = 4ax, a gt 0 be a parabol...

Let `P: y^(2) = 4ax, a gt 0` be a parabola with focus S. Let the tangents to the parabola P make an angle of `(pi)/(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

A

8 only

B

2 only

C

`(1)/(4)` only

D

any `a gt 0`

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