椭圆aX^2+by^2=1与直线y=1-x交于A.B两点,过原点与线段AB中点的直线的斜率为2分之根3,则b/a的值是多少

联立椭圆方程与直线方程：ax^2+b(1-x)^2=1(a+b)x^2-2bx+b-1=0xA+xB=2b/(a+b)yA+yB=1-xA+1-xB=2-2b/(a+b)=2a/(a+b)AB中点坐标：(b/(a+b),a/(a+b))AB中点与原点连线的斜率k=a/(a+b)/(b/(a+b))=a/b=(3)^0.5/2所以b/a=2(...