若焦点在x轴
则x^2/a^2+y^2/b^2=1
过(2,0),所以a=2
a^2=4
e^2=c^2/a^2=(a^2-b^2)/a^2=3/4
4a^2-4b^2=3a^2
a^2=4b^2=4
b^2=1
所以x^2/4+y^2=1
若焦点在y轴
x^2/b^2+y^2/a^2=1
过(2,0),所以b=2,b^2=4
e^2=c^2/a^2=(a^2-b^2)/a^2=3/4
a^2=4b^2=4*4=16
x^2/4+y^2/16=1
所以
x^2/4+y^2=1和x^2/4+y^2/16=1