JEE Main 2021MathematicsEllipseMediumMCQ

JEE Main 2021 — Ellipse Question with Solution

JEE Main 2021 (31 Aug Shift 1)

Question

The line 12x cosθ+5y sinθ=60 is tangent to which of the following curves ?

Choose an option

Show full solutionCorrect option: B
Correct answer
B144x2+25y2=3600

Step-by-step explanation

Given that 12x cosθ+5y sinθ=60

Divide the above equation with 60 on both sides

x cosθ5+y sinθ12=1…i

 Let ellipse x2a2+y2b2=1

⇒ Equation of tangent at point (acosθ,bsinθ)
xa cosθa2+yb sinθb2=1

xcosθa+ysinθb=1…ii

Using equation i and ii⇒a=5
b=12
Equation of ellipse is x225+y2144=1

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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.