∵ If two circles cut orthogonally. ‌⇒2g1g2+2f1f2=c1c2 ‌S1:x2+y2−2y−3=0 ‌S2:x2+y2+4x+3=0 ‌S3:x2+y2−2αx−2βx+c=0⟶‌ centre ‌ ‌(α,β) ‌∴2(−α)(0)+2(−β)(−1)=c−3 ‌‌‌2β=c−3‌‌‌⋅⋅⋅⋅⋅⋅⋅(i) And2(−α)(2)+2β(0)=c+3 −4α=c+3⇒4α=−c−3‌‌‌⋅⋅⋅⋅⋅⋅⋅(ii) On adding Eqs. (i) and (ii), we get ‌4α+2β=−6 ⇒‌‌2α+β=−3
