If \( S \) and \( S^{\prime} \) are the foci, \( C \) is the center, and \( P \) is a point on a...

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If \( S \) and \( S^{\prime} \) are the foci, \( C \) is the center, and \( P \) is a point on a rectangular hyperbola, show that \( S P \times S^{\prime} P=(C P)^{2} \).
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