A line passes through the origin and makes equal angles with the … - Vidyadip

MCQ

A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines
$
L_1: 2 x+y+6=0 \text { and } L_2: 4 x+2 y-p=0, p>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

A
5
B
4
C
2
D
3

✓

Answer

Line is $y=x$
$
\begin{array}{l}
m_1=1, m_2=-2 \\
\text { so } \tan \theta=\left|\frac{1+2}{1-2}\right| \\
\tan \theta=\frac{AM}{BM}=3
\end{array}
$

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