A) \[{{x}^{2}}+{{y}^{2}}-4y=0\]
B) \[{{x}^{2}}+{{y}^{2}}-4|y|=0\]
C) \[{{x}^{2}}+{{y}^{2}}-4x=0\]
D) \[{{x}^{2}}+{{y}^{2}}-4|x|=0\]
Correct Answer: B
Solution :
Let the required point be \[({{x}_{1}},\,{{y}_{1}})\]. Then, according to question, \[4|{{y}_{1}}|=(x_{1}^{2}+y_{1}^{2})\] Þ \[x_{1}^{2}+y_{1}^{2}-4\,\left| {{y}_{1}} \right|=0\] Replace \[({{x}_{1}},\,{{y}_{1}})\] from \[(x,\,y)\], then \[{{x}^{2}}+{{y}^{2}}-4y=0\] is the required locus.
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