x^2/a^2+y^2/b^2=1
b=3 e^2=c^2/b^2=(b^2-a^2)/b^2=1-a^2/b^2=8/9
1-a^2/9=8/9 a^2=1 a=1
所以x^2+y^2/9=1
设直线AB中点为P(-1/2,m)
AB:y-m=k(x+1/2)
y=m+k(x+1/2)
x^2+(m+k(x+1/2))^2/9=1
x^2+k^2(x^2+x+1/4)/9 +m^2/9+2mk(x+1/2)/9-1=0
x^2(k^2/9+1) +x(k^2/9+2mk/9)+m^2/9+k^2/36+mk/9-1=0
x1+x2=-(k^2/9+2mk/9)/(k^2/9+1) =-1
k^2/9+2mk/9=k^2/9+1
2mk=9 .(1)
k=9/(2m)
其中x=-1/2时 1/4+y^2/9=1 y^2/9=3/4 y^2=27/4
-3/2*根号3=