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Let \( E_{1} \) and \( E_{2} \) be two ellipses whose centers are at
P the origin. The major axes of \( E_{1} \) and \( E_{2} \) lie along the

W \( x \)-axis and the \( y \)-axis, respectively. Let \( S \) be the circle \( x^{2}+(y-1)^{2}=2 \). The straight-line \( x+y=3 \) touches the curves \( S, E_{1} \) and \( E_{2} \) at \( P, Q \) and \( R \) respectively. Suppose that \( P Q=P R=\frac{2 \sqrt{2}}{3} \). If \( e_{1} \) and \( e_{2} \) are the eccentricities of \( E_{1} \) and \( E_{2} \), respectively, then the correct expression(s) is (are)
(1) \( e_{1}^{2}+e_{2}^{2}=\frac{43}{40} \)
(2) \( e_{1} e_{2}=\frac{\sqrt{7}}{2 \sqrt{10}} \)
(3) \( \quad\left|e_{1}^{2}-e_{2}^{2}\right|=\frac{5}{8} \)
(4) \( e_{1} e_{2}=\frac{\sqrt{3}}{4} \)
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