JEE Main 2021MathematicsEllipseHardMCQ

JEE Main 2021 — Ellipse Question with Solution

JEE Main 2021 (25 Jul Shift 2)

Question

If a tangent to the ellipse x2+4y2=4 meets the tangents at the extremities of its major axis at B and C, then the circle with BC as diameter passes through the point.

Choose an option

Show full solutionCorrect option: A
Correct answer
A3,0

Step-by-step explanation

We have, x24+y21=1

Equation of tangent is cosθx+2sinθy=2

B-2,1+cosθsinθ,C2,1-cosθsinθ

≡B-2,cotθ2,C2,tanθ2

Equation of required circle will be

x+2x-2+y-cotθ2y-tanθ2=0

⇒x2-4+y2-tanθ2+cotθ2y+1=0

Hence, 3,0 satisfies the above equation.

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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.