Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
If the angle between the asymptotes of a hyperbola is $30^{\circ}$ then its eccentricity is
MathematicsHyperbolaTS EAMCETTS EAMCET 2023 (14 May Shift 1)
Options:
  • A $\sqrt{5}-\sqrt{2}$
  • B $\sqrt{6}-\sqrt{3}$
  • C $\sqrt{5}-\sqrt{3}$
  • D $\sqrt{6}-\sqrt{2}$
Solution:
1292 Upvotes Verified Answer
The correct answer is: $\sqrt{6}-\sqrt{2}$
Angle between asymptotes of hyperbola $=2 \sec ^{-1}(e)$
$\begin{aligned} & 30^{\circ}=2 \sec ^{-1} e \Rightarrow \sec ^{-1} e=15^{\circ} \\ & \therefore e=\sec 15^{\circ} \\ & e=\sqrt{6}-\sqrt{2}\end{aligned}$

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.