Question

If the eccentricity of a hyperbola is $ \sqrt{3}, $ then the eccentricity of its conjugate hyperbola is

• A. $ \sqrt{2} $
• B. $ \sqrt{3} $
• C. $ \sqrt{\frac{3}{2}} $
• D. $ 2\sqrt{3} $

Answer 1

Answer: (C)

Let e and e are the eccentricities of a hyperbola and its conjugate hyperbola.
We know that,
$\frac{1}{e^{2}}+\frac{1}{(e')^{2}}=1$
$\Rightarrow \frac{1}{3}+\frac{1}{(e')^{2}}=1$
$\Rightarrow \frac{1}{(e')^{2}}=\frac{2}{3}$
$\Rightarrow e '=\sqrt{\frac{3}{2}}$