## Understanding the Equation: (x + 1)² + (y - 2)² = 9

This equation represents a circle in the standard form of the circle equation:

**(x - h)² + (y - k)² = r²**

Where:

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

Let's break down our equation:

**(x + 1)²:**This indicates that the x-coordinate of the center is**-1**(since it's written as x + 1, the value of h is -1).**(y - 2)²:**This indicates that the y-coordinate of the center is**2**(since it's written as y - 2, the value of k is 2).**9:**This represents the square of the radius, so the radius is the square root of 9, which is**3**.

### Therefore:

**Center of the circle:**(-1, 2)**Radius of the circle:**3

This information allows us to visualize and plot the circle on a coordinate plane. The center of the circle would be located at the point (-1, 2), and all points on the circle would be exactly 3 units away from this center point.