The correct option is C Centre of S is (-7, 1)
(a)The general equation of a circle is
x2+y2+2gx+2fy+c=0
Where, centre and radius are given by (−g,−f) and √g2+f2−c, respectively.
(b) If the two circles x2+y2+2g1x+2f1y+c1=0 and x2+y2+2g2x+2f2y+c2=0 are orthogonal, then 2g1g2+2f1f2=c1+c2.
Let the circle be x2+y2+2gx+2fy+c=0
It passes through (0, 1).
∴ 1+2f+c=0 ....(i)
Orthogonal with
x2+y2−2x−15=0∴2g(−1)=c−15 using property (b) stated above
⇒ c=15−2g ....(ii)
Similarly,
Orthogonal with x2+y2−1=0
therefore c=1 .....(iii)
Solving (i), (ii) and (iii), we get
⇒ g=7 and f=−1
Centre is (–g,−f)=(−7,1)
∴ Radius = √g2+f2−c
=√49+1−1=7