Question

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. \(e>\frac{2}{\sqrt{3}}\)

Hint:

Use parametric coordinates and equilateral triangle property.

Answer 1

The Correct Option is D