Answer:
[tex](x-2)^{2}[/tex] + [tex](y + 1)^{2}[/tex] = 9
Step-by-step explanation:
The basic equation for the area of a circle is:
[tex](x - h)^{2}[/tex] + [tex](y - k)^{2}[/tex] = [tex]r^{2}[/tex], where h is the x-variable of the center, k is the y-variable of the center, and r is the value of the radius.
From the picture of the circle, we can see that the coordinates of the center are (2, -1) and the radius is 3. We can then substitute this into the basic equation:
[tex](x-2)^{2}[/tex] + [tex](y + 1)^{2}[/tex] = [tex]3^{2}[/tex]
Finally, simplify the right side of the equation:
[tex](x-2)^{2}[/tex] + [tex](y + 1)^{2}[/tex] = 9
