Final answer:
The center of the circle is (2, 0) and the radius is 1. This was determined by comparing the given circle equation with the general form of a circle's equation and simplifying.
Step-by-step explanation:
The equation of the circle is given as 2(x-2)²+2y²=2. To find the center (h, k) and the radius (r) of the circle, we can first simplify the equation by dividing every term by 2 to remove the coefficient on the left side of the equation.
The simplified equation is (x-2)²+y²=1. Now, the general form of a circle's equation is (x-h)²+(y-k)²=r², where (h, k) is the center and r is the radius of the circle.
Comparing the simplified equation with the general form, we identify h=2, k=0, and r²=1. Therefore, the center of the circle is (2, 0) and the radius is 1.