JEE Main 2021MathematicsEllipseMediumMCQ

JEE Main 2021 — Ellipse Question with Solution

JEE Main 2021 (18 Mar Shift 2)

Question

Let a tangent be drawn to the ellipse x227+y2=1 at (33cosθ,sinθ) where θ∈0,π2. Then the value of θ such that the sum of intercepts on axes made by this tangent is minimum is equal to :

Choose an option

Show full solutionCorrect option: C
Correct answer
Cπ6

Step-by-step explanation

Equation of tangent be

xcosθ33+y·sinθ1=1,  θ∈0,π2

intercept on x-axis

OA=33secθ

intercept on y-axis

OB=cosecθ

Now, sum of intercept

=33secθ+cosecθ=f(θ) let

f'(θ)=33secθtanθ-cosecθcotθ

=33sinθcos2θ-cosθsin2θ

=cosθsin2θ·33⏟⊕tan3θ-133=0⇒θ=π6

⇒ at θ=π6,fθ is minimum.

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About this question

This is a previous-year question from JEE Main 2021, 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.