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 $\frac{\pi}{4}$ with the line $y=3 x+5$ touch the parabola $\mathbf{P}$ at $A$ and $B$. Then the value of $a$ for which $A, B$ and $S$ are collinear is:
