JEE Previous Year Question

The focus of the parabola $y^2=4x+16$ 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 $3x-y=0$ and $x+\text{λy}=4$, are ${\lambda }_1$ and ${\lambda }_2\text{,}{\lambda }_1<{\lambda }_2$, then $12{\lambda }_1+29{\lambda }_2$ is equal to

Topic: JEE PYQ

Answer: 15. Full step-by-step solution below.