question_answer

If\[PQ\]is a double ordinate of the 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) \[1<e<\frac{2}{\sqrt{3}}\]           

B)        \[e=\frac{2}{\sqrt{3}}\]

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

D)        \[e>\frac{2}{\sqrt{3}}\]