Answer
Center of circle is $\left( 5,0 \right)$ and radius is $r=\frac{1}{2}$.
Work Step by Step
Standard equation of the circle is:
${{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}}$ (equation - 1)
And equation of circle is ${{\left( x-5 \right)}^{2}}+{{y}^{2}}=\frac{1}{4}$ (equation - 2)
Now compare both the equations.
$\begin{align}
& {{\left( x-5 \right)}^{2}}+{{y}^{2}}=\frac{1}{4} \\
& {{\left( x-\left( 5 \right) \right)}^{2}}+{{\left( y-\left( 0 \right) \right)}^{2}}={{\left( \frac{1}{2} \right)}^{2}} \\
\end{align}$
Center coordinate of circle is $\left( h=5,k=0 \right)$.
And radius of the circle is $r=\frac{1}{2}$.
To graph, we plot the points $\left( 5,0.7071 \right)$, $\left( 5,-0.7073 \right)$, $\left( 4.293,0 \right)$, and $\left( 5.707,0 \right)$ which are, respectively, $\frac{1}{2}$ units above, below, left and right of $\left( 5,0 \right)$.
