双曲线方程:x^2-y^2/3=1,
设A(x1,y1),B(x2,y2),P(x0,y0)
x0=(x1+x2)/2,y0=(y1+y2)/2,
x0=2,y0=1,
x1^2-y1^2/3=1,(1)
x2^2-y2^2/3=1,(2)
(1)-(2)式,
1-(1/3)[(y1-y2)/(x1-x2)][(y1+y2)/2]/[(x1+x2)/2]=0.
其中直线斜率k=(y1-y2)/(x1-x2)
3-k*1/2=0,
k=6,
∴直线方程为:(y-1)=6(x-2),
y=6x-11.
代入双曲线方程,
3x^2-(6x-11)^2=3,
33x^2-132x+124=0,
根据韦达定理,x1+x2=4,
x1x2=124/33,
根据弦长公式,
|AB|=√(1+6^2)(x1-x2)^2=√37*[(x1+x2)^2-4x1x2]
=√[37*(16-124*4/33)]
=√(37*32/33)
=4√2442/33.