设过A(2,1)的直线方程是y-1=k(x-2)
即有y=kx-2k+1
代入到双曲线中有:3x^2-(kx-2k+1)^2=3
3x^2-(k^2x^2+4k^2+1-4k^2x+2kx-4k)-3=0
(3-k^2)x^2+(4k^2-2k)x-4k^2+4k-4=0
x1+x2=(2k-4k^2)/(3-k^2)
又有x1+x2=2*2=4
故有2k-4k^2=12-4k^2
k=6
即直线方程是y=6x-11
代入到双曲线中有:3x^2-(36x^2-132x+121)=3
33x^2-132x+124=0
x1x2=124/33
(x1-x2)^2=(x1+x2)^2-4x1x2=16-4*124/33=32/33
NM=根号(1+K^2)*|x1-x2|=根号(1+36)*根号(32/33)=4根号(74/33)