TS EAMCET · Maths · Hyperbola
A hyperbola having its centre at the origin is passing through the point \((5,2)\) and has transverse axis of length 8 along the \(\mathrm{X}\)-axis. Then the eccentricity of its conjugate hyperbola is
- A \(\frac{\sqrt{13}}{3}\)
- B \(\sqrt{\frac{13}{3}}\)
- C \(\frac{\sqrt{13}}{2}\)
- D \(\sqrt{\frac{13}{2}}\)
Answer & Solution
Correct Answer
(C) \(\frac{\sqrt{13}}{2}\)
Step-by-step Solution
Detailed explanation
Let equation of hyperbola is \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) Given, \(2 \mathrm{a}=8 \Rightarrow \mathrm{a}=4\) It passes through \((5,2)\) Hence, on solving we get, \(\mathrm{b}=\frac{8}{3}\) Now, eccentricity of its conjugate hyperbola is…
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