WBJEE · Maths · Hyperbola
The length of conjugate axis of a hyperbola is greater than the length of transverse axis. Then, the eccentricity e is
- A \(=\sqrt{2}\)
- B \(>\sqrt{2}\)
- C \( < \sqrt{2}\)
- D \( < \frac{1}{\sqrt{2}}\)
Answer & Solution
Correct Answer
(B) \(>\sqrt{2}\)
Step-by-step Solution
Detailed explanation
Let the length of conjugate axis \(=b\) and the length of transvers axis \(=a\) Given that, \(b>a\) Now,\(b^{2}>a^{2}\) \(\therefore\) Eccentricity \((e)=\sqrt{1+\frac{b^{2}}{a^{2}}}\) \(e^{2}=\left(\sqrt{1+\frac{b^{2}}{a^{2}}}\right)^{2}>2\) \(e>\sqrt{2}\)
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