## Understanding the Equation (x+2)^2 + (y-3)^2 = 25

The equation **(x+2)^2 + (y-3)^2 = 25** represents a circle in the coordinate plane. Let's break down why:

### The Standard Form of a Circle

The general equation for a circle with center (h, k) and radius r is:

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

### Analyzing our Equation

By comparing our given equation with the standard form, we can identify the key features:

**Center:**The center of the circle is at**(-2, 3)**. Notice the signs are opposite in the equation (x + 2) and (y - 3).**Radius:**The radius of the circle is**5**. This is because 25 is the square of the radius (r^2 = 25, so r = 5).

### Visualizing the Circle

To graph the circle, we can follow these steps:

**Plot the center:**Locate the point (-2, 3) on the coordinate plane.**Radius points:**Since the radius is 5, move 5 units to the right, left, up, and down from the center to find four points on the circle.**Connect the points:**Draw a smooth curve connecting the points to form the circle.

### Key Takeaways

Understanding the standard form of a circle equation allows us to quickly identify the center and radius, making it easy to visualize and graph the circle. The equation (x+2)^2 + (y-3)^2 = 25 defines a circle with a center at (-2, 3) and a radius of 5 units.