JEE Mains · Maths · STD 11 - 9. straight line
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
- A \(5\)
- B \(4\)
- C \(2\)
- D \(3\)
Answer & Solution
Correct Answer
(D) \(3\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Line is } \mathrm{y}=\mathrm{x} \\ & \mathrm{m}_1=1, \mathrm{~m}_2=-2 \\ & \text { so } \tan \theta=\left|\frac{1+2}{1-2}\right| \\ & \tan \theta=\frac{\mathrm{AM}}{\mathrm{BM}}=3\end{aligned}\)
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