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…

A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines $\displaystyle \mathrm{L}_1: 2 x+y+6=0$ and $\displaystyle \mathrm{L}_2: 4 x+2 y-p=0, p>0$, at the points A and B , respectively. If $\displaystyle \mathrm{AB}=\frac{9}{\sqrt{2}}$ and the foot of the perpendicular from the point A on the line $\displaystyle L_2$ is M, then $\displaystyle \frac{\mathrm{AM}}{\mathrm{BM}}$ is equal to