## Understanding the Equation: (x + 15)² + (y + 5)² = 81

The equation (x + 15)² + (y + 5)² = 81 represents a **circle** in the **Cartesian coordinate system**. To understand this, let's break down the components:

### The Standard Form of a Circle

The general equation of a circle in standard form is:

**(x - h)² + (y - k)² = r²**

Where:

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

### Applying the Standard Form

Comparing our equation (x + 15)² + (y + 5)² = 81 to the standard form, we can identify the following:

**Center:**Since the equation has (x + 15) and (y + 5), the center of the circle is**(-15, -5)**.**Radius:**The right side of the equation is 81, which is the square of the radius. Therefore, the radius of the circle is**√81 = 9**.

### Visualizing the Circle

Knowing the center and radius, we can easily visualize the circle on a coordinate plane. The circle will be centered at (-15, -5) and have a radius of 9 units.

### Key Takeaways

- The equation (x + 15)² + (y + 5)² = 81 represents a circle centered at (-15, -5) with a radius of 9.
- By understanding the standard form of a circle equation, we can quickly identify the center and radius of any given circle.

This equation is a powerful tool to understand and visualize circles, which are fundamental geometric shapes with numerous applications in various fields.