TS EAMCET · Maths · Hyperbola
Let \(x\) be the eccentricity of a hyperbola whose transverse axis is twice its conjugate axis. Let \(y\) be the eccentricity of another hyperbola for which the distance between the focii is 3 times the distance between its directrices. Then \(y^2-x^2=\)
- A \(\frac{23}{16}\)
- B \(\frac{7}{4}\)
- C \(\frac{4}{7}\)
- D \(\frac{16}{23}\)
Answer & Solution
Correct Answer
(B) \(\frac{7}{4}\)
Step-by-step Solution
Detailed explanation
Let the eccentricity of the first hyperbola be \(x\). Transverse axis \(2a\), conjugate axis \(2b\). \(2a = 2(2b) \implies a = 2b\) \(x^2 = 1 + \frac{b^2}{a^2} = 1 + \frac{b^2}{(2b)^2} = 1 + \frac{1}{4} = \frac{5}{4}\) Let the eccentricity of the second hyperbola be \(y\).…
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