右准线方程:x=a^2/c,a^2/c=1,a^2=c,
离心率e=c/a=√3/3,
a=√3c,
(√3c)^2=c,
c=1/3,
a=√3/3,
b=√2/3,
则椭圆方程为:3x^2+9y^2/2=1.