A line passes through the origin and makes equal angles with the...

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