question_answer

The circle \[{{x}^{2}}+{{y}^{2}}+4x-4y+4=0\]t touches:

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.