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Dear Karthik
let centroid of circle is (l,m)
then point A and B will be as shown in figure
and center of circle will be (3l/2 ,3m/2)
so (3k)2 =(3l/2)2 +(3m/2)2
(2k)2 =(l)2 +(m)2
so locus
x2 +y2 =4k2
Regards
Arun(askIITians forum expert)
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