A) \[{{x}^{2}}+{{y}^{2}}=0\]
B) \[{{x}^{2}}+{{y}^{2}}=\]a non-zero constant
C) \[{{x}^{2}}-{{y}^{2}}=0\]
D) \[{{x}^{2}}-{{y}^{2}}=\]a non-zero constant
Correct Answer: C
Solution :
As centres lie on angle bisectors of co-ordinate axes or \[x=0\] and \[y=0,\] we get two lines which are perpendicular to each other on which the centres lie i.e. \[x=y\] and \[x=-y\] or \[{{x}^{2}}-{{y}^{2}}=0\] as combined equation.
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