7、 直线 x=1+t,y=-2+t (t为参数)与椭圆x^2+2y^2=8 交于A、B两点,则|AB|等于?

x=1+t,y=-2+tx-y=3y=x-3代入x^2+2x^2-12x+18=83x^2-12x+10=0x1+x2=4,x1*x2=10/3(x1-x2)^2=(x1+x2)^2-4x1*x2=8/3(y1-y2)^2=[(x1-3)-(x2-3)]^2=(x1-x2)^2=8/3所以|AB|^2=(x1-x2)^2+(y1-y2)^2=16/3|AB|=4根号3/3