A circle of radius `2` units touches the co ordinate 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

Options

A. `x^(2)+y^(2)-4(x+y)-8pi x + (4pi + 1)^(2)=0`
B. `x^(2)+y^(2)-4x-4y+(4 pi + 2)^(2)=0`
C. `x^(2)+y^(2)-8 pi x - 4y+(4 pi + 2)^(2)=0`
D. none of these

Answer

A

Explanation

The old circle has centre at (2, 2) and at (2, 2) and radius 2. After one complete rotation on the x-axis in the positive direction of x-axis, the circle in its new position has centre at `(4 pi + 2, 2)` and same radius.

So, its equation is `{x-(4pi+2)}^(2)+(y-2)^(2)=2^(2)`
`rArr x^(2)+y^(2)-8pi x-4 (x+y)+(4pi + 2)^(2)=0`