A) \[{{x}^{2}}+{{y}^{2}}-\alpha x-\beta y=0\]
B) \[{{x}^{2}}+{{y}^{2}}+2\alpha x+2\beta y=0\]
C) \[{{x}^{2}}+{{y}^{2}}-2\alpha x-2\beta y=0\]
D) \[{{x}^{2}}+{{y}^{2}}+\alpha x+\beta y=0\]
Correct Answer: C
Solution :
Radius = Distance from origin \[=\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\] \[\therefore \] \[{{(x-\alpha )}^{2}}+{{(y-\beta )}^{2}}={{\alpha }^{2}}+{{\beta }^{2}}\] \[\Rightarrow {{x}^{2}}+{{y}^{2}}-2\alpha x-2\beta y=0\].
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