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设弦AB，A（x1,y1),B(x2,y2),∵A、B均在椭圆上，∴x1^2/16+y1^2/4=1,(1)x2^2/16+y2^2/4=1,(2)(1)-(2)式，（x1^2-x2^2)/16+(y1^2-y2^2)/4=1,1/4+[(y1-y2)/(x1-x2)]*[(y1+y2)/2]/[(x1+x2)/2]=0,其中(y1-y2)/(x1-x2)为直线的斜率k，（y1+y2)/2，（x1+x2)/2为AB中点M的纵、横坐标，1/4+k*(1/2)=0,∴k=-1/2,∴弦直线方程为：(y-1)/(x-2)=-1/2,即：x+2y-4=0... |
