Concept:The equation of a circle is (x−a)2+(y−b)2=r2, where (a,b) is the center and r is the radius.Explanation:Rewrite the given equation by grouping the x and y terms.x2+y2−8x−2y+1=0Complete the square for the x terms.x2−8x=(x−4)2−16Complete the square for the y terms.y2−2y=(y−1)2−1Substitute these into the given equation.(x−4)2−16+(y−1)2−1+1=0(x−4)2+(y−1)2−16=0(x−4)2+(y−1)2=16Comparing with (x−a)2+(y−b)2=r2, we get r2=16.So, r=16=4.Answer:The radius of the circle is 4.Correct option: C. 4.