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Question

A circle of radius 14 units touches the coordinate axes in the first quadrant. If the circle makes three complete rolls along positive direction of Y axis, then the equation of circle in the new position is

A
(x14)2+(y278)2=14
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B
(x14)2+(y278)2=196
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C
(x+14)2+(y+278)2=196
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D
(x14)2+(y102)2=196
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Solution

The correct option is B (x14)2+(y278)2=196
Center of the circle in initial position: C1(14,14)
When circle is rolled n complete cycles along positive direction of Yaxis,
New position of centre:
C2(14,14+n(2πr))
Putting n=3, we get
C2(14,14+6π14)C2(14,14+3×2×227×14)C2(14,278)
The radius of the new circle is same as r=14 units

The equation of the required circle is
(x14)2+(y278)2=196

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