#### Answer

See below:

#### Work Step by Step

The circle is centered at $\left( 3,-2 \right)$ in the rectangular plane.
And the radius of the circle is $2$.
Plot the graph of the function ${{\left( x-3 \right)}^{2}}+{{\left( y+2 \right)}^{2}}=4$ as follows:
Step 1:
Plot the center on the coordinate plane; take $2$ units in every direction from the center $\left( h,k \right)=\left( 3,-2 \right)$.
Step 2:
Now, connect the dots using a smooth and round curve to get the graph.
The graph of the function ${{\left( x-3 \right)}^{2}}+{{\left( y+2 \right)}^{2}}=4$ intersect the $x-\text{axis}$ at the point $\left( 3,0 \right)$.