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  4. The length of conjugate axis of a hyperbola is greater than the length of transverse axis. Then the eccentricity e is,

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Q. The length of conjugate axis of a hyperbola is greater than the length of transverse axis. Then the eccentricity e is,

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Solution:

$2b > 2a$ or, $b > a$ or, $b/a > 1$ or, $\frac{b^{2}}{a^{2}} > 1$ or, $e^{2} - 1 > 1 \left[\because b^{2} = a^{2}\left(e^{2}-1\right) \,or, \, \frac{b^{2}}{a^{2}} = e^{2}-1\right]$ or, $e^{2} > 2$ or, $e > \sqrt{2}$