A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines ${{\rm{L}}_1}:2x + y + 6 = 0$ and ${{\rm{L}}_2}:4x + 2y - p = 0,p > 0$, 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