+0

+1
92
2

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Feb 14, 2019

#1
+101871
+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

Feb 14, 2019
#2
+5226
+1

there is no A

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

By rolling two revolutions the circle is displaced two circumferences to the right.

With radius 1 the circumference is 2pi.

The y coordinate of the center doesn't change when rolling horizontally.

Feb 14, 2019