#1**+1 **

Look at the following graph :

The curve formed by a point on the circle as it rotates is known as a "cycloid"...the graph shows two rotations....the y coordinate for the center does not change....the new x value for the center is given by 4pi - sin (4pi) = 4pi So....the correct equation is

(x - 4pi)^2 + ( y - 1)^2 = 1

CPhill Feb 14, 2019