Let c1:x2+y2=1;C2:(x−10)2+y2=1 and C3;x2+y2−10x−42y+457=0 be three circle.A circle C has been drawn to touch circles C1 and C2 externally and C3 internally. Now circles C1,C2 and C3 start rolling on the circumference of circle C in anticlockwise direction with constant speed. The centroid of the triangle formed by joining the centres of rolling circles C1,C2 and C3 lies on
x2+y2−10x−24y+144=0
The equation of circle C is (x−5)2+(y−12)2=122 This circle also touches x - axis at (5,0) From the geometry, centroid lies on the circle (x−5)2+(y−12)2=52