A) \[\left( \frac{1}{4},\ 0 \right)\] and \[\frac{1}{4}\]
B) \[\left( -\frac{1}{2},\ 0 \right)\] and \[\frac{1}{2}\]
C) \[\left( \frac{1}{2},\ 0 \right)\] and \[\frac{1}{2}\]
D) \[\left( 0,\ -\frac{1}{4} \right)\] and \[\frac{1}{4}\]
Correct Answer: A
Solution :
The circle is \[{{x}^{2}}+{{y}^{2}}-\frac{1}{2}x=0\]. Centre \[(-g,\ -f)=\left( \frac{1}{4},\ 0 \right)\] and \[R=\sqrt{\frac{1}{16}+0-0}=\frac{1}{4}\].
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