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

Question

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 $A B = \frac{9}{2}$ and the foot of the perpendicular from the point A on the line $L_{2}$ is $M$ , then $\frac{A M}{BM}$ is equal to

Options:

Answer:

D

Solution:

$Line is y = x m_{1} = 1, m_{2} = - 2 so tan θ = \frac{1 + 2}{1 - 2} tan θ = \frac{AM}{BM} = 3$

TestHub · Accepted Answer

​ Line is y = x m 1 ​ = 1 , m 2 ​ = − 2 so tan θ = ​ 1 − 2 1 + 2 ​ ​ tan θ = BM AM ​ = 3 ​

Mathematics - Straight Lines Question with Solution | TestHub

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JEE Main 2028 (Class 11)