WBJEE · Maths · Hyperbola
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
- A \(1 < e < \frac{2}{\sqrt{3}}\)
- B \(e=\frac{2}{\sqrt{2}}\)
- C \(e=\frac{\sqrt{3}}{2}\)
- D \(e>\frac{2}{\sqrt{3}}\)
Answer & Solution
Correct Answer
(D) \(e>\frac{2}{\sqrt{3}}\)
Step-by-step Solution
Detailed explanation
Given equation of hyperbola is \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) and \(\Delta O P Q\) is an equlateral triangle. \(P Q\) is double ordinate of the hyperbola. Let the coordinates of \(P\) and \(Q\) be \((a \sec \theta, b\) tan \(\theta)\) and \((a \sec \theta,-b\)…
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