JEE Main 2026 — Circle Question with Solution
JEE Main 2026 (24 January Shift 1)
Question
Let a circle of radius 4 pass through the origin O, the points and , where and are real parameters and . Then the locus of the centroid of is a circle of radius
Choose an option
Show full solutionCorrect option: B
Correct answer
B
Step-by-step explanation
Circle of radius 4 passes through O and points A(, 0), B(0, ).
Let center be C(h, k) on circle: .
Since A, B lie on circle: gives
And gives
Centroid G = . Setting and :
and
From : →
Substituting: →
Radius =
Let center be C(h, k) on circle: .
Since A, B lie on circle: gives
And gives
Centroid G = . Setting and :
and
From : →
Substituting: →
Radius =
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This is a previous-year question from JEE Main 2026, covering the Circle 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.