若斜率不存在
则x=1,y^2=32/9,此时中点是(1,0),不成立
y-1=k(x-1)
y=kx+(1-k)
4x^2+9[kx+(1-k)]^2=36
(4+9k^2)x^2+18k(1-k)x+9(1-k)^2-36=0
x1+x2=-18k(1-k)/(4+9k^2)=(18k^2-18k)/(4+9k^2)
中点坐标是x=(x1+x2)/2,y=(y1+y2)/2
所以x1+x2=(18k^2-18k)/(4+9k^2)=1*2
18k^2-18k=8+18k^2
k=-2/9
2x+9y-11=0
x1+x2=(18k^2-18k)/(4+9k^2)=11
x1x2=[9(1-k)^2-36]/(4+9k^2)=-203/40
所以(x1-x2)^2=(x1+x2)^2-4x1x2=11+203/10=313/10
(y1-y2)^2={[kx1+(1-k)]-[kx2+(1-k)]}^2=k^2(x1-x2)^2=1252/810
所以AB^2=(x1-x2)^2+(y1-y2)=5321/162
AB=√10642/18