A circle of radius 14units 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
(x−14)2+(y−278)2=14
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B
(x−14)2+(y−278)2=196
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C
(x+14)2+(y+278)2=196
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D
(x−14)2+(y−102)2=196
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Solution
The correct option is B(x−14)2+(y−278)2=196 Center of the circle in initial position: C1≡(14,14)
When circle is rolled n complete cycles along positive direction of Y−axis,
New position of centre: C2≡(14,14+n(2πr))
Putting n=3, we get ⇒C2≡(14,14+6π⋅14)⇒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 (x−14)2+(y−278)2=196