Centre of S is (-4,1)
Centre of S is (-8,1)
Radius of S is 8
Radius of S is 7
Given circles x²+y²-8x=0, x²+y²=1
Let equation of circle x²+y²+2gx+2fy+c=0
The circle passes through (0,1) ⇒ 1+2f+c=0
Applying condition of orthogonality -8g=c, 0=c
⇒ c=1, g=-1/8, f=-1
r=√(1/64+1) = √65/8; centre(-1/8,-1)