JEE Main 2020MathematicsHyperbolaMediumMCQ

JEE Main 2020 — Hyperbola Question with Solution

JEE Main 2020 (02 Sep Shift 2)

Question

For some θ∈0,π2, if the eccentricity of the hyperbola, x2-y2sec2θ=10 is 5 times the eccentricity of the ellipse, x2sec2θ+y2=5, then the length of the latus rectum of the ellipse, is

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Show full solutionCorrect option: D
Correct answer
D453

Step-by-step explanation

For hyperbola x210-y210cos2θ=1

The eccentricity of the hyperbola eH=1+b2a2=1+cos2θ 

For ellipse x25cos2θ+y25=1

The eccentricity of an ellipse eE=1-b2a2=1-cos2θ=sinθ

Given, eH=5 eE

⇒1+cos2θ=5sin2θ⇒cos2θ=23 

Now, the length of the latus rectum of an ellipse =2b2a=10cos2θ5=2035=453 

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About this question

This is a previous-year question from JEE Main 2020, covering the Hyperbola chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.