JEE Main 2020MathematicsEllipseMediumMCQ

JEE Main 2020 — Ellipse Question with Solution

JEE Main 2020 (04 Sep Shift 2)

Question

Let x=4 be a directrix to an ellipse whose centre is at the origin and its eccentricity is 12. If P(1,β),β>0 is a point on this ellipse, then the equation of the normal to it at P is

Choose an option

Show full solutionCorrect option: D
Correct answer
D4x–2y=1

Step-by-step explanation

ae=4⇒a=4e⇒a=2

b2=a21-e2=3

(1,β) lies on x24+y23=1⇒14+β23=1⇒    β2=94⇒β=32(∵β>0)

Normal at (1,β)⇒ a2x1-b2yβ=a2-b2  ⇒4x-3yβ=1

so equation of normal is 4x-2y=1 

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About this question

This is a previous-year question from JEE Main 2020, covering the Ellipse 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.