A) \[{{k}^{2}}({{x}^{2}}+{{y}^{2}})-{{a}^{2}}=0\]
B) \[{{x}^{2}}+{{y}^{2}}-{{k}^{2}}{{a}^{2}}=0\]
C) \[{{x}^{2}}+{{y}^{2}}+{{a}^{2}}=0\]
D) \[{{x}^{2}}+{{y}^{2}}-{{a}^{2}}=0\]
Correct Answer: D
Solution :
\[{{(x-ak)}^{2}}+{{y}^{2}}={{k}^{2}}\,\left[ {{\left( x-\frac{a}{k} \right)}^{2}}+{{y}^{2}} \right]\] \[\Rightarrow \,\,(1-{{k}^{2}})\,({{x}^{2}}+{{y}^{2}})-2akx+2akx+{{a}^{2}}{{k}^{2}}-{{a}^{2}}=0\] \[\Rightarrow \,\,{{x}^{2}}+{{y}^{2}}-{{a}^{2}}=0\].
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