If $e_{1}$ and $e_{2}$ are ecentricities of the hyperbolas $xy = c^{2}$ and $x^{2} - y^{2} = a^{2}$ then $e_{1}^{2} + e_{2}^{2} =$

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$e_{1}^{2} - e_{2}^{2}$

$e_{1}^{2} e_{2}^{2}$

answer is A.

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Detailed Solution

Since both are rectangular hyperbolas then $e_{1} = e_{2} = \sqrt{2}$

Now $e_{1}^{2} + e_{2}^{2} = 2 + 2 = 4$

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