X^2/4+Y^2/3=1
a^2=4 b^2=3
c^2=a^2-b^2=1
∴右焦点坐标是(1,0)
则那条直线方程是
y-0=1(x-1）
y=x-1代入椭圆方程得
x^2/4+(X-1)^2/3=1
3x^2+4(x^2-2x+1)=12
7x^2-8x-8=0
xa+xb=8/7
xaxb=-8/7
(xa-xb)^2=(xa+xb)^2-4xaxb
=64/49+32/7
=288/49
(ya-yb)^2=(xa-1-xb+1)^2=(xa-xb)^2=288/49
线段AB的长度=√[(xa-xb)^2+(ya-yb)^2]
=√(288/49+288/49)=24/7