设椭圆方程为x^2/a^2+y^2/b^2=1
联立椭圆与抛物线得
(a^2+b^2)*x^2-6a^2*x+9a^2-a^2*b^2=0
所以x(A)+x(B)=6a^2/(a^2+b^2)
y(A)+y(B)=6b^2/(a^2+b^2)
x(A)*x(B)=(9a^2-a^2*b^2)/(a^2+b^2)
得中点C[3a^2/(a^2+b^2),3b^2/(a^2+b^2)]
OC的斜率为2,即b^2/a^2=2
|AB| =根号下[(x(A)-x(B))^2+(y(A)-y(B))^2]
=根号下2*(x(A)-x(B))^2
=根号下2*[(x(A)+x(B))^2-4x(A)*x(B)]
所以a^2=9/2,b^2=9
椭圆方程为2*x^2/9+y^2/9=1