S1≡x2+y2=4...(i) S2≡x2+y2−2x−3=0...(ii) S3≡x2+y2−2y−3=0...(iii) Let S4≡x2+y2+2gx+2fy+c be the circle which is orthogonal with the circles S1,S2 and S3 Condition of orthogonal, 2(gg′+ff′)=c+c′ Now, for S1 and S4 , g×0+f×0=˙c−4 ⇒c=4 For S2 and S4 2[g×(−1)+f×(0)]=4−3 ⇒g=−
1
2
For S3 and S4 2[g×(0)+f×(−1)]=4−3 ⇒f=−
1
2
Now, radius of S4 r2=g2+f2−c=(
1
4
+
1
4
−4)=−
7
2
<0 Thus, no such S4 circle is possible which is orthogonal to S1,S2,S3