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TS EAMCET · Maths · Hyperbola

If the angle between the asymptotes of a hyperbola is \(30^{\circ}\) then its eccentricity is

  1. A \(\sqrt{5}-\sqrt{2}\)
  2. B \(\sqrt{6}-\sqrt{3}\)
  3. C \(\sqrt{5}-\sqrt{3}\)
  4. D \(\sqrt{6}-\sqrt{2}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\sqrt{6}-\sqrt{2}\)

Step-by-step Solution

Detailed explanation

Angle between asymptotes of hyperbola \(=2 \sec ^{-1}(e)\) \(\begin{aligned} & 30^{\circ}=2 \sec ^{-1} e \Rightarrow \sec ^{-1} e=15^{\circ} \\ & \therefore e=\sec 15^{\circ} \\ & e=\sqrt{6}-\sqrt{2}\end{aligned}\)