Mathematics · Straight lines

JEE Main 2025 — 3 April, Morning Shift — Question 32

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

$L_{1}: 2 x+y+6=0$ and $L_{2}: 4 x+2 y-p=0, p>0$ , at the points A and B , respectively. If

$\mathrm{AB}=\frac{9}{\sqrt{2}}$ 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

Answer: D

Line is $\mathrm{y}=\mathrm{x}$

$\mathrm{m}_{1}=1, \mathrm{~m}_{2}=-2$

so $\tan \theta=\left|\frac{1+2}{1-2}\right|$

$\tan \theta=\frac{\mathrm{AM}}{\mathrm{BM}}=3$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 3 April, Morning Shift
Subject: Mathematics
Chapter: Straight lines
Topic: Angle between lines, perpendicular distance & distance between parallel lines, foot, image