JEE Main 2023MathematicsEllipseHardNumerical

JEE Main 2023 — Ellipse Question with Solution

JEE Main 2023 (24 Jan Shift 1)

Question

Let a tangent to the curve 9x2+16y2=144 intersect the coordinate axes at the points A and B. Then, the minimum length of the line segment AB is ______

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Show full solutionCorrect answer: 7
Correct answer
7

Step-by-step explanation

Given:

9x2+16y2=144

⇒x216+y29=1

Equation of tangent at point P4cosθ, 3sinθ is 

xcosθ4+ysinθ3=1

So, A is 4secθ,0 and point B is 0,3cosecθ.

Hence,

AB=16 sec2θ+9cosec2θ

⇒AB=25+16tan2 θ+9cot2 θ

⇒25+16tan2 θ+9cot2 θ≥7

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About this question

This is a previous-year question from JEE Main 2023, 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.