雙曲線x^2-y^2/4=1即4x^2-y^2=4
設(shè)A（x1,y1）B（x2,y2）,直線L上任意一點（x,y）
4x1^2-y1^2=4
4x2^2-y2^2=4
兩式相減
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為直線L.
將4x-y-6=0即y=4x-6代入雙曲線4x^2-y^2=4
整理：3x^2-12x+10=0
韋達(dá)定理：x1+x2=4,x1×x2=10/3
弦長公式：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)怎么來的你可以這樣理解4(x1+x2)-(y1+y2)(y1-y2)/(x1-x2)=016-4(y1-y2)/(x1-x2)=0(y1-y2)/(x1-x2)=4即可知直線L的斜率k=4y-2=4（x-2）y=4x-6