Given the equation of the circle x2+y2−8x−2y+1=0.
The equation of a circle is given as (x−a)2+(y−b)2=r2
Expanding, we have x2−2ax+a2+y2−2by+b2=r2≡x2−2ax+y2−2by=r2−a2−b2
Comparing the RHS of the equation above with the equation rewritten as x2+y2−8x−2y=−1, we have
−2a=−8;−2b=−2impliesa=4,b=1
∴r2−42−12=−1impliesr2=−1+16+1=16
r=√16=4