A circle of radius 2 touches the coordinate axes in the first quadrant. If the circle makes a co...

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A circle of radius 2 touches the coordinate axes in the first quadrant. If the circle makes a complete rotation on the \( x \)-axis along the positive direction of the \( x \)-axis then the equation of the circle in the new position is
(a) \( x^{2}+y^{2}-4(x+y)-8 \pi x+(2+4 \pi)^{2}=0 \)
(b) \( x^{2}+y^{2}-4 x-4 y+(2+4 \pi)^{2}=0 \)
(c) \( x^{2}+y^{2}-8 \pi x-4 y+(2+4 \pi)^{2}=0 \)
(d) none of these
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