已知椭圆x^2/a^2+y^2/b^2=1(a>b>0)与直线x+y-1=0与交于两点A,B,椭圆的...答:(1)c^2=a^2-b^2=1,a^2+c^2=2b^2,得到b^2=2,a^2=3,代入椭圆方程2x^2+3y^2=6 将y=1-x代入,得到5x^2-6x-3=0,x1+x2=6/5,x1*x2=-3/5,同理可得5y^2-4y-4=0,y1+y2=4/5,y1*y2=-4/5,IABI^2=(x2-x1)^2+(y2-y1)^2=(x2+x1)^2+(y2+y1)^2-4x1x...