AP EAMCET · Maths · Hyperbola
If the latus rectum subtends a right angle at center of the hyperbola, then its eccentricity is
- A \(\frac{\sqrt{13}}{2}\)
- B \(\frac{\sqrt{5}-1}{2}\)
- C \(\frac{\sqrt{5}+1}{2}\)
- D \(\frac{\sqrt{3}+1}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{\sqrt{5}+1}{2}\)
Step-by-step Solution
Detailed explanation
Given, latus rectum of hyperbola subtends 90º at its centre. Let there be a hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) So, eccentricity, \(e=\sqrt{1+\frac{b^2}{a^2}}\) End points of latusrectum are…
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