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Question

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


A

x2+y212x22y+144=0

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B

x2+y210x24y+144=0

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C

x2+y28x20y+64=0

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D

x2+y24x2y4=0

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Solution

The correct option is B

x2+y210x24y+144=0


The equation of circle C is (x5)2+(y12)2=122 This circle also touches x - axis at (5,0) From the geometry, centroid lies on the circle (x5)2+(y12)2=52


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