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

Here graph of the circle is given.

we need to match the graph with the correct equation.

Here given equation is${(x-3)}^2+{(y+3)}^2=9$ which is in the standard form of the equation of a circle ${(x-h)}^2+{(y-k)}^2=r^2,here(h,k)iscenterofthecircleandradiusisr$. Thus when we compare the given equation to a standard form of the equation the circle, we get center (h, k) is (3,-3) and radius is 3. Then the graph of the given equation is given below

Here equation of the circle ${(x+1)}^2+{(y-2)}^2=4$, when we compared this to a standard form of the equation of a circle, we can understand that center (h, k) is ((-1,2) and radius is 2. then graph is given here

Here equation of the equation of a circle is ${(x-1)}^2+{(y+2)}^2=4$. From the given equation we get the center (h, k) is (1.-2 and radius is 2 since the given equation is in the form of a standard equation of a circlelocalid="1646168427688" ${\left(x-h\right)}^2+{(y-k)}^2=r^2$. Hence the graph is given below

To plot the graph of the circle we should know the center and radius , here the equation is in the form of the standard form of the equation of a circle ${(x-h)}^2+{(y-k)}^2=r^2$. Thus the center of the circle according to the question is (-3,3) and the radius is 3. Then graph is given below

According to the question, we plotted the graph of the equation for each option and the correct match of equation of the given question graph is option (c)${(x-1)}^2+{(y+2)}^2=4$