If \( e_{1} \) and \( e_{2} \) are the eccentricities of the conic ...

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If \( e_{1} \) and \( e_{2} \) are the eccentricities of the conic
\( \mathrm{P}^{17:} \) sections \( 16 x^{2}+9 y^{2}=144 \) and \( 9 x^{2}-16 y^{2}=144 \), then

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(1) \( e_{1}^{2}+e_{2}^{2}=3 \)
(2) \( e_{1}^{2}+e_{2}^{2}3 \)
(3) \( e_{1}^{2}+e_{2}^{2}3 \)
(4) \( e_{1}^{2}-e_{2}^{2}=1 \)
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