Mathematics Question from JEE Main 2025 · 3 April, Shift 1

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 $AB = \frac{9}{\sqrt{2}}$ and the foot of the perpendicular from the point A on the line $L_2$ is M, then $\frac{AM}{BM}$ is equal to