A) \[{{x}^{2}}+{{y}^{2}}-6x+2y-6=0\]
B) \[{{x}^{2}}+{{y}^{2}}-6=0\]
C) \[{{x}^{2}}+{{y}^{2}}-3x+y-6=0\]
D) \[{{x}^{2}}+{{y}^{2}}=0\]
E) \[{{x}^{2}}-{{y}^{2}}-6x-2y-8=0\]
Correct Answer: A
Solution :
Let\[z=x+iy\] \[\therefore \] \[|z-3+i|=|x+iy-3+i|\] \[=|x-3+i(1+y)|\] \[\Rightarrow \] \[{{(x-3)}^{2}}+{{(1+y)}^{2}}=16\] (given) \[\Rightarrow \]\[{{x}^{2}}+{{y}^{2}}-6x+2y-6=0\]is the required locus.
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