A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines
$\mathrm{L}_1: 2 \mathrm{x}+\mathrm{y}+6=0$ and $\mathrm{L}_2: 4 \mathrm{x}+2 \mathrm{y}-\mathrm{p}=0, \mathrm{p} \gt 0$, at the points $A$ and $B$, respectively. If $A B=\frac{9}{\sqrt{2}}$ and the foot of the perpendicular from the point A on the line $L_2$ is $M$, then $\frac{A M}{B M}$ is equal to

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Aicharya · Accepted Answer

$\begin{aligned} & 	ext { Line is } \mathrm{y}=\mathrm{x} \ & \mathrm{m}_1=1, \mathrm{~m}_2=-2 \ & 	ext { so } 	an 	heta=\left|\frac{1+2}{1-2}ight| \ & 	an 	heta=\frac{\mathrm{AM}}{\mathrm{BM}}=3\end{aligned}$ .

A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the…

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