The coordinate of point P is (x0,-6/x0); Then A(0, -6/x0), B(x0, 0)

M(-3，0)，N(0，√3)； E(-6√3/x0-3, -6/x0) is composed of y=√3x/3+√3 and y=-6/x0.

Then find F(x0, √3x0/3+√3), and use the formula of two-point distance to get:

me=√[(-3+6√3/x0+3)^2+(0+6/x0)^2]= 12/|x0|

nf=√[(x0-0)^2+(√3x 0/3+√3-√3)^2]=(2√3/3)|x0|

So there is: ME*NF=8√3.