Q. 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) $2\sqrt{3}$
Explanation
(c)
Let $e$ and $e'$ are the eccentricities of a hyperbola and its conjugate hyperbola.
Then, $\frac{1}{e^{2}} + \frac{1}{\left( e^{'} \right)^{2}} = 1 \Rightarrow \ \frac{\ 1}{3} + \frac{1}{\left( e^{'} \right)^{2}} = 1 \Rightarrow \ e^{'} = \sqrt{\frac{3}{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.