AP EAMCET · Maths · Hyperbola
For a hyberbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\), if the length of the transvere axis is 8 and the distance between the foci is \(2 \sqrt{41}\), then the length of its latus rectum is
- A \(\frac{25}{2}\)
- B \(\frac{32}{5}\)
- C \(\frac{25}{4}\)
- D \(\frac{16}{5}\)
Answer & Solution
Correct Answer
(A) \(\frac{25}{2}\)
Step-by-step Solution
Detailed explanation
Given, \(2 a=8\) \(\Rightarrow \quad a=4\) \(\therefore \quad 2 a e=2 \sqrt{41}\) \(\Rightarrow \quad a e=\sqrt{41}\) \(\because \quad a^2 e^2=a^2+b^2\) \(41=16+b^2\) \(\Rightarrow \quad b^2=25\) Length of latus rectum \(=\frac{2 b^2}{a}\) \(=\frac{2 \times 25}{4}=\frac{25}{2}\)
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