COMEDK · Maths · 15. Hyperbola
If \(e_{1}\) and \(e_{2}\) are the eccentricities of a hyperbola \(3 x^{2}-3 y^{2}=25\) and its conjugate, then
- A \(e_{1}^{2}+e_{2}^{2}=2\)
- B \(e_{1}^{2}+e_{2}^{2}=4\)
- C \(e_{1}+e_{2}=4\)
- D \(e_{1}+e_{2}=\sqrt{2}\)
Answer & Solution
Correct Answer
(B) \(e_{1}^{2}+e_{2}^{2}=4\)
Step-by-step Solution
Detailed explanation
We have, equation of hyperbola \[ \begin{gathered} 3 x^{2}-2 j^{2}=25 \\ \Rightarrow \quad \frac{x^{2}}{\left(\frac{5}{\sqrt{3}}\right)^{2}}-\frac{y^{2}}{\left(\frac{5}{\sqrt{2}}\right)^{2}}=1 \end{gathered} \] Equation of conjugate hyperbola is…
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