If the point of intersection of the tangents drawn at the points where the line  $5x+y+1=0$cuts the circle $x^2+y^2-2x-6y-8=0$ is (a, b) then 5a + b = 
 

Chord of contact of (a, b) w.r.t to circle

 $$\begin{gathered} {\mathrm{x}}^2+{\mathrm{y}}^2-2\mathrm{x}-6\mathrm{y}-8=0 \mathrm{is} {\mathrm{S}}_1=0 \\ \mathrm{x}(\mathrm{a}-1)+\mathrm{y}(\mathrm{b}-3)-\mathrm{a}-3\mathrm{b}-8=0 -\left(1\right) \end{gathered}$$

Given line 

 $5\mathrm{x}+\mathrm{y}+1=0 -\left(2\right)$

Both represent same line then 

we get  a=-9, b=1

$$\begin{gathered} 5a+\mathrm{b}=-45+1 \\ =-44 \end{gathered}$$