JEE Main 2025 — 23 January, Evening Shift — Question 23

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 $3 \mathrm{x}-\mathrm{y}=0$ and $\mathrm{x}+\lambda \mathrm{y}=4$, are $\lambda_{1}$ and $\lambda_{2}, \lambda_{1}<\lambda_{2}$, then $12 \lambda_{1}+29 \lambda_{2}$ is equal to $\_\_\_\_\_$ .