Official solution
Let \[{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1(a < b)\] is the equation of ellipse, focii \[(0, \pm 2)\]
Given 2a = 4 \[ \Rightarrow \] a = 2
e2 = 1 - \[{{{a^2}} \over {{b^2}}}\] \[ \Rightarrow \] b2e2 = b2 - a2
4 = b2 - 4
b2 = 8
\[ \because \] equation of ellipse is \[{{{x^2}} \over 4} + {{{y^2}} \over 8} = 1\]
then it passes through \[\left( {\sqrt 2 ,2} \right)\]