If \(P Q\) is a double ordinate of the hyperbola \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) such that \(\Delta O P Q\) is equilateral, \(O\) being the centre. Then the eccentricity e satisfies

Question

If \(P Q\) is a double ordinate of the hyperbola \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) such that \(\triangle O P Q\) is equilateral, \(O\) being the centre. Then the eccentricity e satisfies
(A) \(1<\mathrm{e}<\frac{2}{\sqrt{3}}\)
(B) \(e=\frac{2}{\sqrt{2}}\)
(C) \(e=\frac{\sqrt{3}}{2}\)
(D) \(e>\frac{2}{\sqrt{3}}\)

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