If a circle of a constant radius 6 passes through origin O and meets the coordinate axes at A and B , then find the locus of the centroid of O A B .

Step-by-step solution

Let (h, k) be centroid of triangle h= a 3 and k= b 3 a=3 h, b=3 k Now, A B is diameter of circle. aligned & a^2+b^2=144 & (3 h)^2+(3 k)^2=144 h^2+k^2= 144 9 aligned h^2+k^2=16 Locus of centroid of O A B is x^2+y^2=16