A) \[\sqrt{2}\]
B) \[\sqrt{3}\]
C) \[\sqrt{\frac{3}{2}}\]
D) \[2\sqrt{3}\]
Correct Answer: C
Solution :
Let e and e are the eccentricities of a hyperbola and its conjugate hyperbola. We know that, \[\frac{1}{{{e}^{2}}}+\frac{1}{{{(e)}^{2}}}=1\] \[\Rightarrow \] \[\frac{1}{3}+\frac{1}{{{(e)}^{2}}}=1\] \[\Rightarrow \] \[\frac{1}{{{(e)}^{2}}}=\frac{2}{3}\Rightarrow e=\sqrt{\frac{3}{2}}\]
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