A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines L₁: 2x+y+6=0 and L₂: 4x+2y-p=0, p>0, at the points A and B, respectively. If AB=9/(√(2)) and the foot of the perpendicular from the point A on the line L₂ is M, then AM/BM is equal to:

Coordinate Geometry: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q88

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumCoordinate Geometry478× since 2002

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

L_1:\;2x+y+6=0

and

L_2:\;4x+2y-p=0,\;p>0

, at the points

A

and

B

, respectively. If

AB=\tfrac{9}{\sqrt{2}}

and the foot of the perpendicular from the point

A

on the line

L_2

M

, then

\tfrac{AM}{BM}

is equal to:

JEE Main 2025 Coordinate Geometry Question with Solution (April Unspecified (session-level dataset), Q88) | JEE Arc