JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If a hyperbola has length of its conjugate axis equal to \(5\) and the distance between its foci is \(13\), then the eccentricity of the hyperbola is
- A \(\frac{{13}}{{12}}\)
- B \(2\)
- C \(\frac{{13}}{{6}}\)
- D \(\frac{{13}}{{8}}\)
Answer & Solution
Correct Answer
(A) \(\frac{{13}}{{12}}\)
Step-by-step Solution
Detailed explanation
\(2b = 5\) and \(2ae = 13\) \({\left( {ae} \right)^2} = {a^2} + {b^2}\) \( \Rightarrow {a^2} = {\left( {ae} \right)^2} - {b^2} = \frac{{169}}{4} - \frac{{25}}{4}\) \( \Rightarrow a = 6\) \(e = \frac{{ae}}{a} = \frac{{13}}{{12}}\)
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