Question

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

• A. $=\sqrt{2}$
• B. $>\sqrt{2}$
• C. $<\sqrt{2}$
• D. $\frac{1}{\sqrt{2}}$

Answer 1

The correct option is B $>\sqrt{2}$

$b>a\Rightarrow \frac{b^2}{a^2}>1$
$\Rightarrow 1+\frac{b^2}{a^2}>2$
$\Rightarrow e^2>2\Rightarrow e>\sqrt{2}$