Question

If a circle of constant radius 3k passes through the origin and meets the axes at a and b the locus of the centeroid of the triangle abc is.

Answer 1

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Answer 2

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