TS EAMCET · Maths · Hyperbola
If the angle between the asymptotes of a hyperbola is \(30^{\circ}\) then its eccentricity is
- A \(\sqrt{5}-\sqrt{2}\)
- B \(\sqrt{6}-\sqrt{3}\)
- C \(\sqrt{5}-\sqrt{3}\)
- D \(\sqrt{6}-\sqrt{2}\)
Answer & Solution
Correct Answer
(D) \(\sqrt{6}-\sqrt{2}\)
Step-by-step Solution
Detailed explanation
Angle between asymptotes of hyperbola \(=2 \sec ^{-1}(e)\) \(\begin{aligned} & 30^{\circ}=2 \sec ^{-1} e \Rightarrow \sec ^{-1} e=15^{\circ} \\ & \therefore e=\sec 15^{\circ} \\ & e=\sqrt{6}-\sqrt{2}\end{aligned}\)
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