match each graph with the correct equation.$$\begin{gathered} \left(a\right){(x-3)}^2+{(y+3)}^2=9,\left(b\right){(x+1)}^2+{(y-2)}^2=4, \\ \left(c\right){(x-1)}^2+{(y+2)}^2=4,\left(d\right){(x+3)}^2+{(y-3)}^2=9 \end{gathered}$$

The graph of the circle is given.

we need to match the graph with the correct equation.

The given equation of a circle is ${(x-3)}^2+{(y+3)}^2=9$ which is in the standard form of the equation of a circle

Thus here center is (h, k ) is (3,-3) and radius is 3. Then the graph of the equation${(x-3)}^2+{(y+3)}^2=9.$is given below

Here equation of the circle is ${(x+1)}^2+{(y-2)}^2=4$.while comparing this equation to a standard form of the equation of a circle , we get center is (-1,2) and radius is 4. Using this we can plot the graph of the circle ,the plotted graph is given below

we know that the standard form of the equation of a circle is ${(x-h)}^2+{(y-k)}^2=r^2$.

The given equation is ${(x-1)}^2+{(y+2)}^2=4$, when comparing given equation to the standard equation, then the center becomes (1,-2) and radius will become 2. Thus the graph of the circle is given below

when we compared ${(x+3)}^2+{(y-3)}^2=9$to the standard form of the equation of circle we get center is (-3,3) and radius is 3.Now we can plot the graph , that is given below

The sketched graph of the equation for each option and the correct match of the equation of the given question graph is option (d)${(x+3)}^2+{(y-3)}^2=9$