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]

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

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

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

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

Two circles \[{{S}_{1}}={{x}^{2}}+{{y}^{2}}+2{{g}_{1}}x+2{{f}_{1}}y+{{

1.	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.	\[2{{g}_{1}}{{g}_{2}}-2{{f}_{1}}{{f}_{2}}={{c}_{1}}-{{c}_{2}}\]
Answer» B. \[2{{g}_{1}}{{g}_{2}}-2{{f}_{1}}{{f}_{2}}={{c}_{1}}+{{c}_{2}}\]

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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]

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