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JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Hyperbola

JEE Main · Mathematics · Hyperbola

The length of conjugate axis of a hyperbola is greater than the...

The length of conjugate axis of a hyperbola is greater than the length of transverse axis. Then, the eccentricity e is

Options

  1. A=2=\sqrt{2}
  2. B>2>\sqrt{2}
  3. C<2< \sqrt{2}
  4. D<12< \frac{1}{\sqrt{2}}

Correct answer

B. >2>\sqrt{2}

Step-by-step solution

Let the length of conjugate axis =b=b and the length of transvers axis =a=a Given that, b>ab>a Now,b2>a2∴b^{2}>a^{2}\therefore Eccentricity (e)=1+b2a2e2=(1+b2a2)2>2e>2(e)=\sqrt{1+\frac{b^{2}}{a^{2}}}e^{2}=\left(\sqrt{1+\frac{b^{2}}{a^{2}}}\right)^{2}>2e>\sqrt{2}
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