Question

A circle of radius $2$ touches the coordinates axes in the first quadrant. If the circle makes the 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. $x^2+y^2-4x-4y+{(2+4\pi )}^2=0$
• C. $x^2+y^2-8\pi x-4y+{(2+4\pi )}^2=0$
• D. none of these

Answer 1

The correct option is A $x^2+y^2-4(x+y)-8\pi x+{(2+4\pi )}^2=0$

The center of the circle with radius $2$ in the initial position will be $(2,2)$
Since, it makes complete rotation along X-axis, its new co-ordinate will be $(2+4\pi ,2)$
Therefore, equation of circle will be $(x-2-4\pi {)}^2+(y-2{)}^2=4$