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  4. If e and e1 are the eccentricities of the hyperbolas xy = c2 and x2 - y2 = c2, then e2 + e1 2 is equal to

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Q. If $e $ and $ e_1$ are the eccentricities of the hyperbolas $xy = c^2$ and $ x^2 - y^2 = c^2,$ then $ e^2 + e_1\,{}^2$ is equal to

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Solution:

$e=\sqrt{2}, e_{1} = \sqrt{2}$
$\therefore e^{2}+e_{1}^{2} = 2+2=4$