question_answer

Two circles \[{{S}_{1}}={{x}^{2}}+{{y}^{2}}+2{{g}_{1}}x+2{{f}_{1}}y+{{c}_{1}}=0\] and \[{{S}_{2}}={{x}^{2}}+{{y}^{2}}+2{{g}_{2}}x+2{{f}_{2}}y+{{c}_{2}}=0\]cut each other orthogonally, then [RPET 1995]

A)            \[2{{g}_{1}}{{g}_{2}}+2{{f}_{1}}{{f}_{2}}={{c}_{1}}+{{c}_{2}}\]     

B)            \[2{{g}_{1}}{{g}_{2}}-2{{f}_{1}}{{f}_{2}}={{c}_{1}}+{{c}_{2}}\]

C)            \[2{{g}_{1}}{{g}_{2}}+2{{f}_{1}}{{f}_{2}}={{c}_{1}}-{{c}_{2}}\]       

D)            \[2{{g}_{1}}{{g}_{2}}-2{{f}_{1}}{{f}_{2}}={{c}_{1}}-{{c}_{2}}\]