The focus of the parabola y^2=4 x+16 is the centre of the circle C of radius 5 .

Question

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 $\lambda_1$

Accepted Answer

${y}^{2}=4(x+4)$

Equation of circle

$(x+3{)}^{2}+{y}^{2}=25$

Passes through the point of intersection of two lines $3x-y=0$ and $x+\lambda y=4$ which is $(\frac{4}{3\lambda +1},\frac{12}{3\lambda +1})$, after solving with circle, we get

$\begin{gathered} \lambda =-\frac{7}{6},1 \ 12{\lambda }_{1}+29{\lambda }_{2} \ -14+29=15 \end{gathered}$

Solutions · 1