If $e_1, e_2$ are respectively the eccentricities of the curves $9 x^2-16 y^2-144=0$ and $9 x^2-16 y^2+144=0$, then $\frac{e_1^2 e_2^2}{e_1^2+e_2^2}=$

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Aicharya · Accepted Answer

(i) is a hyperbola and (ii) is a conjugate hyperbola, We have, $ \begin{array}{ll} \therefore & \frac{1}{e_1^2}+\frac{1}{e_2^2}=1 \\ \therefore & \frac{e_1^2+e_2^2}{e_1^2 e_2^2}=1 \Rightarrow \frac{e_1^2 e_2^2}{e_1^2+e_2^2}=1 \end{array} $ Hence, option (b) is correct

If $e_1, e_2$ are respectively the eccentricities of the curves $9 x^2-16 y^2-144=0$ and $9 x^2-16…

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