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JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
The eccentricity of the hyperbola whose length of the latus rectum is equal to \(8\) and the length of its conjugate axis is equal to half of the distance between its foci is :
- A \(\frac{2}{{\sqrt 3 }}\;\)
- B \(\sqrt 3 \)
- C \(\frac{4}{3}\)
- D \(\frac{4}{{\sqrt 3 }}\)
Answer & Solution
Correct Answer
(A) \(\frac{2}{{\sqrt 3 }}\;\)
Step-by-step Solution
Detailed explanation
We have \(\frac{2 b^{2}}{a}=8\) and \(2 b=\frac{1}{2}(2 a e)\) \(\therefore \frac{2}{a}\left(\frac{a e}{2}\right)^{2}=8\) \(a e^{2}=16--(1)\) Now \(\frac{2 b^{2}}{a}=8\) \(b^{2}=4 a\) \(a^{2}\left(e^{2}-1\right)=4 a\) \(a e^{2}-a=4\) Substitute the value of \(a e^{2}=16\) in eq…
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