## Understanding the Equation and its Circumference

The equation **(x + 2)^2 + (y - 3)^2 = 9** represents a circle in the standard form of the circle equation:

**(x - h)^2 + (y - k)^2 = r^2**

Where:

**(h, k)**represents the center of the circle.**r**represents the radius of the circle.

From our given equation, we can identify:

**Center:**(-2, 3)**Radius:**√9 = 3

**Therefore, the circle represented by the equation has a center at (-2, 3) and a radius of 3.**

### Calculating the Circumference

The circumference of a circle is the distance around its boundary. It is calculated using the formula:

**Circumference (C) = 2πr**

Where:

**π (pi)**is a mathematical constant approximately equal to 3.14159**r**is the radius of the circle.

Using the radius of our circle (r = 3), we can calculate its circumference:

**C = 2π(3) = 6π**

**Therefore, the circumference of the circle represented by the equation (x + 2)^2 + (y - 3)^2 = 9 is 6π units.**