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If \( P \) is a point on the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \), whose foci
\( \mathrm{P} \) are \( S \) and \( S^{\prime} \). Let \( \angle P S S^{\prime}=\theta \) and \( \angle P S^{\prime} S=\phi \), then

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\( \begin{array}{ll}\text { (a) } S P+S^{\prime} P=2 a \text {, if } ab & \text { (b) } S P+S^{\prime} P=2 b \text {, if } ba\end{array} \)
(c) \( \tan \left(\frac{\theta}{2}\right) \tan \left(\frac{\phi}{2}\right)=\frac{1-e}{1+e} \) (d) \( \tan \left(\frac{\theta}{2}\right) \tan \left(\frac{\phi}{2}\right)=\frac{e-1}{e+1} \)
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