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If \( e \) and \( e^{\prime} \) are the eccentricities of the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) and \( \frac{y^{2}}{b^{2}}-\frac{x^{2}}{a^{2}}=1 \), then the point
\( \mathrm{P} \) \( \left(\frac{1}{e}, \frac{1}{e^{\prime}}\right) \) lies on the circle:

W
(A) \( x^{2}+y^{2}=1 \)
(B) \( x^{2}+y^{2}=2 \)
(C) \( x^{2}+y^{2}=3 \)
(D) \( x^{2}+y^{2}=4 \)
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