question_answer

The equations of the circles which touch both the axes and the line \[x=a\] are

A)  \[{{x}^{2}}+{{y}^{2}}\pm ax\pm ay+\frac{{{a}^{2}}}{4}=0\]

B) \[{{x}^{2}}+{{y}^{2}}+ax\pm ay+\frac{{{a}^{2}}}{4}=0\]

C)  \[{{x}^{2}}+{{y}^{2}}-ax\pm ay+\frac{{{a}^{2}}}{4}=0\]

D)  None of these

Correct Answer: C

Solution :

\[\Rightarrow \] \[{{\left( x-\frac{a}{2} \right)}^{2}}+{{\left( y\pm \,\frac{a}{2} \right)}^{2}}={{\left( \frac{a}{2} \right)}^{2}}\] \[\Rightarrow \] \[{{x}^{2}}+{{y}^{2}}-ax\pm \,ay+\frac{{{a}^{2}}}{4}=0\]