Question

The eccentricity of the hyperbola can never be equal to-

• A. $\sqrt{\frac{9}{5}}$
• B. $2\sqrt{\frac{1}{9}}$
• C. $3\sqrt{\frac{1}{8}}$
• D. $\sqrt{2}$

Answer 1

The correct option is B $2\sqrt{\frac{1}{9}}$

we know that eccentricity of hyperbola is greater than 1.
so, $\sqrt{\frac{9}{5}}=\frac{3}{\sqrt{5}}>1$
$2\sqrt{\frac{1}{9}}=2\times \frac{1}{3}=\frac{2}{3}<1$
so, $2\sqrt{\frac{1}{9}}$
$3\sqrt{\frac{1}{8}}=\frac{3}{2\sqrt{2}}>1$
$\sqrt{2}=1.414>1$

$\therefore$ The eccentricity of the hyperbola can never be equal to $\sqrt{2}$