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Question

A circle of radius 7 units touches the coordinate axes in the second quadrant. If the circle makes five complete rolls along the positive direction of xaxis, then the equation of circle in new position is
(Assume π=227)

A
(x+227)2+(y7)2=49
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B
(x213)2+(y7)2=49
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C
(x227)2+(y+7)2=49
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D
(x+213)2+(y+7)2=49
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Solution

The correct option is B (x213)2+(y7)2=49
Given radius, r=7
Centre of the circle in initial position : C1(7,7)

When circle rolls five complete cycle along positive direction of x-axis, new position of centre is,
C2(7+5×2πr,7)
C2(7+5×2×227×7,7)(213,7)
and r=7 (fixed)
Required equation of the circle is
(x213)2+(y7)2=49

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