A(x1,y1) B(x2,y2)
则x1+x2=4 y1+y2=2
又因为A,B在双曲线上
x1^2-y1^1/3=1
x2^2-y2^2/3=1
两式相减得
(x1+x2)(x1-x2)-(y1+y2)(y1-y2)/3=0
将x1+x2=4 y1+y2=2代入 得
y1-y2/x1-x2=6
即斜率为6