A) \[{{x}^{2}}+{{y}^{2}}+4x-21=0\]
B) \[{{x}^{2}}+{{y}^{2}}+4x+21=0\]
C) \[{{x}^{2}}+{{y}^{2}}-4x-21=0\]
D) \[{{x}^{2}}+{{y}^{2}}+5x-21=0\]
Correct Answer: A
Solution :
Let centre be\[(-g,\ 0)\], then \[\sqrt{{{g}^{2}}-c}=5\Rightarrow c={{g}^{2}}-25\] Also it passes through (2, 3), therefore \[13+4g+{{g}^{2}}-25=0\Rightarrow g=-6,\ 2\] Hence the equations are \[{{x}^{2}}+{{y}^{2}}-12x+11=0\] and \[{{x}^{2}}+{{y}^{2}}+4x-21=0\].
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