A) \[{{x}^{2}}+3{{y}^{2}}=0\]
B) \[{{x}^{2}}-3{{y}^{2}}=0\]
C) \[3{{x}^{2}}+{{y}^{2}}=0\]
D) \[3{{x}^{2}}-{{y}^{2}}=0\]
Correct Answer: B
Solution :
Let the moving point be (x, y) and its distance from x-axis is y. Therefore, according to given condition \[\frac{1}{2}\sqrt{{{x}^{2}}+{{y}^{2}}}=y\,\,\,\Rightarrow \,\,{{x}^{2}}-3{{y}^{2}}=0\] This is required locus of the point (x, y).
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