Let P: y^2=4 a x, a>0 be a parabola with focus S. Let the tangents to the parabola P make an angle of (π)/4 with the line y=3 x+5 touch the parabola…

Let $\displaystyle \mathrm{P}: y^2=4 a x, a>0$ be a parabola with focus S . Let the tangents to the parabola P make an angle of $\displaystyle \frac{\pi}{4}$ with the line $\displaystyle y=3 x+5$ touch the parabola P at A and B . Then the value of $\displaystyle a$ for which $\displaystyle \mathrm{A}, \mathrm{B}$ and S are collinear is