If the lines $x^2+2 x y-35 y^2-4 x+44 y-12=0$ and $5 x+\lambda y-8=0$ are concurrent, then the value of $\lambda$ is

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Aicharya · Accepted Answer

Given line is $x^2+2 x y-35 y^2-4 x+44 y-12=0$ Here, $a=1, b=-35, c=-12, h=1, f=22$, $g=-2$ $	herefore$ Point of intersection is $\left(\frac{h f-b g}{a b-h^2}, \frac{g h-a f}{a b-h^2}ight)$ $=\left(\frac{22-70}{-35-1}, \frac{-2-22}{-35-1}ight)$ $\begin{aligned} & =\left(\frac{48}{36}, \frac{24}{36}ight) \ & =\left(\frac{4}{3}, \frac{2}{3}ight)\end{aligned}$ If the lines are concurrent Then, $5\left(\frac{4}{3}ight)+\lambda\left(\frac{2}{3}ight)-8=0$ $\begin{array}{ll}\Rightarrow & \frac{2}{3} \lambda=8-\frac{20}{3} \ \Rightarrow & \lambda=\frac{24-20}{3} 	imes \frac{3}{2} \ \Rightarrow & \lambda=2\end{array}$

If the lines $x^2+2 x y-35 y^2-4 x+44 y-12=0$ and $5 x+\lambda y-8=0$ are concurrent, then the value of…

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