A) \[z\bar{z}-z{{\bar{z}}_{0}}-\bar{z}{{z}_{0}}+{{z}_{0}}{{\bar{z}}_{0}}={{r}^{2}}\]
B) \[z\bar{z}+z{{\bar{z}}_{0}}-\bar{z}{{z}_{0}}+{{z}_{0}}{{\bar{z}}_{0}}={{r}^{2}}\]
C) \[z\bar{z}-z{{\bar{z}}_{0}}+\bar{z}{{z}_{0}}-{{z}_{0}}{{\bar{z}}_{0}}={{r}^{2}}\]
D) None of these
Correct Answer: A
Solution :
Equation of circle \[|z-{{z}_{0}}{{|}^{2}}={{r}^{2}}\] \[\Rightarrow \,(z-{{z}_{0}})\,(\overline{z-{{z}_{0}}})={{r}^{2}}\]\[\Rightarrow \,(z-{{z}_{0}})\,(\bar{z}-{{\bar{z}}_{0}})=\,{{r}^{2}}\] \[z\bar{z}-z{{\bar{z}}_{0}}-\bar{z}{{z}_{0}}+{{z}_{0}}{{\bar{z}}_{0}}={{r}^{2}}\].
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