Consider the lines $\mathrm{x}(3 \lambda+1)+\mathrm{y}(7 \lambda+2)=17 \lambda+5$, $\lambda$ being a parameter, all passing through a point P . One of these lines (say L) is farthest from the origin. If the distance of $L$ from the point $(3,6)$ is $d$, then the value of $d^2$ is

Question

Aicharya · Accepted Answer

$\begin{aligned}
& \mathrm{x}(3 \lambda+1)+\mathrm{y}(7 \lambda+2)=17 \lambda+5 \\ & (\mathrm{x}+2 \mathrm{y}-5)+\lambda(3 \mathrm{x}+7 \mathrm{y}-17)=0
\end{aligned}$
intersection of family of lines
$\mathrm{P}(1,2)$
Let $\mathrm{Q}(3,6)$
$\begin{aligned}
& \mathrm{d}=\mathrm{PQ}=\sqrt{2^2+4^2}=\sqrt{20} \\ & \mathrm{~d}^2=20
\end{aligned}$
option (1) .

Consider the lines $\mathrm{x}(3 \lambda+1)+\mathrm{y}(7 \lambda+2)=17 \lambda+5$, $\lambda$ being a…

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