A) \[x-\]axis
B) \[y-\]axis
C) \[x-\] axis and \[y-\]axis
D) none of the above
Correct Answer: C
Solution :
Key Idea: If any circle touches the coordinate axes, then radius of circle is equal to the perpendicular distance from centre to the coordinate axes. Equation of circle is \[{{x}^{2}}+{{y}^{2}}+4x-4y+4=0\] Centre is \[(-2,2)\] And radius\[=\sqrt{4+4-4}=2\] \[\Rightarrow \]Circle touches both the axes. Alternate Solution: Equation of circle is \[{{x}^{2}}+{{y}^{2}}+4x-4y+4=0\] \[({{x}^{2}}+4x+4)+({{y}^{2}}-4y+4)+4-4-4=0\] \[\Rightarrow \] \[{{(x+2)}^{2}}+{{(y-2)}^{2}}={{2}^{2}}\] It is clear from the figure that circle touch both the coordinate axes.You need to login to perform this action.
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