Question

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

Short answer

The matched equation of the given graph is option (d)${\left(x+3\right)}^2+{(y-3)}^2=9$

Step-by-step solution

Step 1. Given information

The graph of the circle is given.

we need to match the graph with the correct equation.

. Plot the graph of option (a)(x-3)2+(y+3)2=9

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

Step 3. Plot the graph of  option (b) (x+1)2+(y-2)2=4

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

Step 4. Sketch the graph of option (c) x-12+(y+2)2=4

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

Step 5. Sketch the graph of option (d)(x+3)2+(y-3)2=9

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

step 6. Matching the correct equation

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