举报
99111445
设AB:y=x+m, 代入椭圆方程得3x^2+5(x^2+2mx+m^2)=30, 8x^2+10mx+5m^2-30=0, 设A(x1,y1),B(x2,y2),则 x1+x2=-5m/4,x1x2=(5m^2-30)/8. 以AB为直径的圆恰好过椭圆C的中心O(0,0), ∴OA*OB=x1x2+y1y2 =x1x2+(x1+m)(x2+m) =2x1x2+m(x1+x2)+m^2 =(5m^2-30-5m^2)/4+m^2=0, ∴m=土√30/2, ∴直线L的方程为y=x土√30/2.