a circle passes through origin meets the axes at A and B so that (2,3) lies on AB then the locus of centroid of triangle OAB

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)}