If \( \mathrm{e} \) and \( e \) ' are the eccentricities of hyperbo...

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If \( \mathrm{e} \) and \( e \) ' are the eccentricities of hyperbola and its
\( \mathrm{P} \) conjugate respectively, then:

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(1) \( ₫\left(\frac{1}{e}\right)^{2}+\left(\frac{1}{e^{\prime}}\right)^{2}=1 \)
(2) \( \frac{1}{e}+\frac{1}{e^{\prime}}=1 \)
(3) \( \frac{1}{e^{2}}+\frac{1}{\left(e^{\prime}\right)^{2}}=0 \)
(4) \( \frac{1}{e}+\frac{1}{e^{\prime}}=2 \)
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