Answer
Center of the circle is $\left( 0,1 \right)$ and radius is $r=\frac{1}{5}$
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 the equation of the circle is ${{x}^{2}}+{{\left( y-1 \right)}^{2}}=\frac{1}{25}$ (equation - 2)
Now compare both the equations.
$\begin{align}
& {{x}^{2}}+{{\left( y-1 \right)}^{2}}=\frac{1}{25} \\
& {{\left( x-\left( 0 \right) \right)}^{2}}+{{\left( y-\left( 1 \right) \right)}^{2}}={{\left( \frac{1}{5} \right)}^{2}} \\
\end{align}$
Center coordinate of circle is $\left( h=0,k=1 \right)$.
And radius of circle is $r=\frac{1}{5}$.
To graph, we plot the points $\left( 0,1.45 \right)$, $\left( 0,0.55 \right)$, $\left( -0.45,1 \right)$, and $\left( 0.45,1 \right)$ which are, respectively, $\frac{1}{5}$ units above, below, left and right of $\left( 0,1 \right)$.
