圆转化为标准方程：(x-2)^2+(y-1)^2=5/2,
圆心C（2,1）,半径R=√10/2,
椭圆离心率e=c/a=√3/2,
b^2=a^2-c^2=a^2-3a^2/4=a^2/4,
设椭圆方程为：x^2/a^2+4y^2/a^2=1,
∵AB是直径,则C是AB的中点,
设A（x1,y1),B(x2,y2),
(x1+x2)/2=2,x2=4-x1,
(y1+y2)/2=1,y1=2-y2,
x1^2/a^2+4y1^2/a^2=1,(1)
(4-x1)^2/a^2+4(2-y1)^2/a^2=1,(2)
(1)和（2）式联立消去a,
x1+2y1=4,(3)
(x1-2)^2+(y1-1)^2=5/2,(4)
由（3）代入（4）式,
x1=5,y1=-1/2,
则AB方程为：(y-1)/(x-2)=(-1/2-1)/(5-2),
x+2y-4=0,
代入椭圆方程,
5^2/a^2+4*(-1/2)^2/a^2=1,
a^2=26,
b^2=a^2/4=13/2,
∴椭圆方程为：x^2/26+2y^2/13=1.