Let E1 and E2, be two ellipses whose centers are at the origin.The major axes of E1 and E2, lie along the x-axis and the y-axis, respectively. Let S be the circle $x^2+{\left(y-1\right)}^2=2$. The straight line x+ y =3 touches the curves S, E1 and E2 at P,Q and R, respectively. Suppose that $PQ=PR=\frac{2\sqrt{2}}{3}$.If e1 and e2 are the eccentricities of E1 and E2, respectively, then the correct expression(s) is(are):

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