JEE Main 2024MathematicsEllipseMediumMCQ

JEE Main 2024 — Ellipse Question with Solution

JEE Main 2024 (27 Jan Shift 1)

Question

The length of the chord of the ellipse x225+y216=1, whose mid point is 1,25, is equal to:

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Show full solutionCorrect option: A
Correct answer
A16915

Step-by-step explanation

Equation of chord with given middle point is given by,

T=S1

⇒x25+y40=125+1100

⇒8x+5y200=8+2200

⇒y=10-8x5   ..i

⇒x225+(10-8x)2400=1

⇒16x2+100+64x2-160x400=1

⇒4x2-8x-15=0

⇒x=8±3048

⇒x1=8+3048; x2=8-3048

Similarly, y=10-8±3045=2±3045

⇒y1=2-3045;y2=2+3045

Distance =x1-x22+y1-y22

=4×30464+4×30425

=16915

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About this question

This is a previous-year question from JEE Main 2024, 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.