If \( \alpha, \beta \) are the ends of a focal chord of an ellipse ...

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If \( \alpha, \beta \) are the ends of a focal chord of an ellipse of eccentricity e, then \( \tan \frac{\alpha}{2} \cdot \tan \frac{\beta}{2} \) is
\( \mathrm{P} \) equal to
(A) \( \frac{1-\mathrm{e}}{1+\mathrm{e}} \)
(B) \( \frac{1+\mathrm{e}}{1-\mathrm{e}} \)
(C) \( \frac{e-1}{e+1} \)
(D) \( \frac{e+1}{e-1} \)
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