圆C1:(x-2)^2+(y-1)^2=20/3,与C2相交于A,B两点,且线段AB恰为C1的直径,可知C1(2,1)是AB的中点,则
xA+xB=2xC1=2*2=4,yA+yB=2,k(AB)=(yA-yB)/(xA-xB)
椭圆C2:x^2/a^2+y^2/b^2=1(a>b>0)
e=√2/2
a^2=2c^2=2(a^2-b^2)
a^2=2b^2
x^2/a^2+y^2/b^2=1
b^2*x^2+2b^2*y^2=2b^4
x^2+2y^2=2b^2
(xA)^2+2(yA)^2=2b^2.(1)
(xB)^2+2(yB)^2=2b^2.(2)
(1)-(2):
(xA+xB)*(xA-xB)+2(yA+yB)*(yA-yB)=0
(xA+xB)+2(yA+yB)*(yA-yB)/(xA-xB)=0
4+2*2*k(AB)=0
k(AB)=-1
AB的方程:x+y-3=0
y=3-x代入园C1的方程,可得A,B的坐标,把A,B中其中一个点的坐标代入椭圆方程,可求b^2=,a^2=2b^2=
即可得椭圆方程,请自己计算,并检验题目是否有问题.