Mathematics · 2020
JEE Main · 2 September 2020, Shift 2 · Q66
For some θ ∈(0, (π)/2), if the eccentricity of the hyperbola, x^2-y^2 sec^2 θ=10 is √ 5 times the eccentricity of the ellipse, x^2 sec^2 θ+y^2=5,…
For some $\displaystyle \theta \in\left(0, \frac{\pi}{2}\right)$, if the eccentricity of the hyperbola, $\displaystyle x^2-y^2 \sec ^2 \theta=10$ is $\displaystyle \sqrt{5}$ times the eccentricity of the ellipse, $\displaystyle x^2 \sec ^2 \theta+y^2=5$, then the length of the latus rectum of the ellipse, is :
Official answer
(3)
$\displaystyle \frac{4 \sqrt{5}}{3}$
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JEE Main 2020 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.