question_answer

If PQ is a double ordinate of hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] such that OPQ is an equilateral triangle, O being the centre of the hyperbola. Then the eccentricity e of the hyperbola satisfies

A)  \[1<e<2\text{/}\sqrt{3}\]          

B)  \[e=2\text{/}\sqrt{3}\]

C)  \[e=\frac{\sqrt{3}}{2}\]                        

D)  \[e>2\text{/}\sqrt{3}\]

E)  None of these