x^2/8-y^2=1 a=2√2 b=1 c^2=a^2+b^2=9 c=3 焦点（3,0）（-3,0） 过（3,0）的直线方程 y/(x-3)=1/n x=ny+3 (ny+3)^2-8y^2=8 (n^2-8)y^2+6ny+1=0
y1+y2=-6n/(n^2-8) y1*y2=1/(n^2-8)
设截得的弦长为AB A（x1,y1）,B(x2,y2) AB^2=(x1-x2)^2+(y1-y2)^2 x1-x2=ny1-ny2
AB^2=(1+n^2)(y1-y2)^2=(1+n^2)[(y1+y2)^2-4y1y2]=(1+n^2)[36n^2/(n^2-8)^2--4/(n^2-8)]
=(1+n^2)[(36n^2)-4n^2+32]/(n^2-8)^2=32[1+n^2]^2/(n^2-8)^2
已知弦长为根号2/2 即AB^2=1/2=32[1+n^2]^2/(n^2-8)^2 [1+n^2]^2/(n^2-8)^2=1/64
[1+n^2]/(n^2-8)=+-1/8 取+ 无解 取负 n=0
说明直线垂直X轴且过焦点,则此直线方程是x=3 或x=--3
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