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 \[(h,\,k)\] be the point. According to question \[4\,\sqrt{{{(h-h)}^{2}}+{{k}^{2}}}={{h}^{2}}+{{k}^{2}}\] \[\Rightarrow \] \[4\,\,\left| k \right|={{h}^{2}}+{{k}^{2}}\] Locus of the point is \[\Rightarrow \] \[4\,\,\left| y \right|={{x}^{2}}+{{y}^{2}}\] \[\Rightarrow \] \[{{x}^{2}}+{{y}^{2}}-4\,\left| y \right|=0\]
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