JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
For some \(\theta \in\left(0, \frac{\pi}{2}\right),\) if the eccentricity of the hyperbola, \(x^{2}-y^{2} \sec ^{2} \theta=10\) is \(\sqrt{5}\) times the eccentricity of the ellipse, \(x^{2} \sec ^{2} \theta+y^{2}=5,\) then the length of the latus rectum of the ellipse is
- A \(\sqrt{30}\)
- B \(\frac{4 \sqrt{5}}{3}\)
- C \(2 \sqrt{6}\)
- D \(\frac{2 \sqrt{5}}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{4 \sqrt{5}}{3}\)
Step-by-step Solution
Detailed explanation
Given \(\theta \in\left(0, \frac{\pi}{2}\right)\) equation of hyperbola \(\Rightarrow x^{2}-y^{2} \sec ^{2} \theta=10\) \(\Rightarrow \frac{x^{2}}{10}-\frac{y^{2}}{10 \cos ^{2} \theta}=1\) Hence eccentricity of hyperbola…
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