双曲线x^2-y^2/4=1即4x^2-y^2=4
设A（x1,y1）B（x2,y2）,直线L上任意一点（x,y）
4x1^2-y1^2=4
4x2^2-y2^2=4
两式相减
4(x1+x2)(x1-x2)-(y1+y2)(y1-y2)=0
4(x1+x2)-(y1+y2)(y1-y2)/(x1-x2)=0
x1+x2=4,y1+y2=4,(y1-y2)/(x1-x2)=(y-2)/(x-2)
所以4-(y-2)/(x-2)=0
即4x-y-6=0为直线L.
将4x-y-6=0即y=4x-6代入双曲线4x^2-y^2=4
整理：3x^2-12x+10=0
韦达定理：x1+x2=4,x1×x2=10/3
弦长公式：AB=√(1+k^2)[(x1+x2)^2-4x1x2]=√(1+16)[16-4*10/3]=2√102/3(y1-y2)/(x1-x2)=(y-2)/(x-2)怎么来的你可以这样理解4(x1+x2)-(y1+y2)(y1-y2)/(x1-x2)=016-4(y1-y2)/(x1-x2)=0(y1-y2)/(x1-x2)=4即可知直线L的斜率k=4y-2=4（x-2）y=4x-6