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Standard Equation of Hyperbola

If e and ...

Question

If $e$ and $e_{1}$ are the eccentricities of the hyperbola $x y = c^{2}$ and $x^{2} - y^{2} = c^{2}$ , then $e^{2} + e_{1}^{2} = ?$

A

1

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B

4

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C

6

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D

8

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Solution

The correct option is B $4$
As both the hyperbola are rectangular. Hence,
$e = e_{1} = \sqrt{2}$
Hence,
$e^{2} + e_{1}^{2} = 4$

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