AP EAMCET · Maths · Hyperbola
If the eccentricity of a hyperbola is \(\frac{5}{3}\), then the eccentricity of its conjugate hyperbola is
- A \(\frac{5}{3}\)
- B \(\frac{5}{4}\)
- C \(\frac{5}{2}\)
- D \(\frac{8}{5}\)
Answer & Solution
Correct Answer
(B) \(\frac{5}{4}\)
Step-by-step Solution
Detailed explanation
Eccentricity of given hyperbola \(=\frac{5}{3}\) Let, eccentricity of its conjugate hyperbola \(=e\) So, \(\frac{1}{\left(\frac{5}{3}\right)^2}+\frac{1}{e^2}=1\) \(\Rightarrow \quad \frac{9}{25}+\frac{1}{e^2}=1 \quad \Rightarrow \frac{1}{e^2}=1-\frac{9}{25}\)…
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