The focus of the parabola $y^{2}=4 x+16$ is the centre of the circle $C$ of radius 5 . If the values of $\lambda$, for which $C$ passes through the point of intersection of the lines $3 x-y=0$ and $x+\lambda y=4$, are $\lambda_{1}$ and $\lambda_{2}, \lambda_{1}<\lambda_{2}$, then $12 \lambda_{1}+29 \lambda_{2}$ is equal to $\_\_\_\_$ .