## Unveiling the Secrets of (x+1)^2 + (y-3)^2 = 49

The equation (x+1)^2 + (y-3)^2 = 49 represents a **circle** in the **Cartesian coordinate system**. Let's dive into its properties and understand how to interpret this equation.

### The Standard Equation of a Circle

The general standard form for the equation of a circle is:

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

Where:

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

### Analyzing our Equation

Comparing our equation (x+1)^2 + (y-3)^2 = 49 to the standard form, we can identify the following:

**Center:**(h, k) =**(-1, 3)****Radius:**r^2 = 49 => r =**7**

### Visualizing the Circle

With the center and radius in hand, we can easily visualize the circle on a graph:

**Plot the center:**Locate the point (-1, 3) on the coordinate plane.**Draw the circle:**Starting from the center, draw a circle with a radius of 7 units.

### Key Points to Remember

- The equation (x+1)^2 + (y-3)^2 = 49 describes a circle with its
**center at (-1, 3)**and**radius of 7 units**. - The
**standard form of the circle equation**is a powerful tool for understanding and graphing circles. - Understanding the relationship between the equation and its corresponding geometric shape allows for deeper insights into mathematical concepts.

By analyzing the equation (x+1)^2 + (y-3)^2 = 49, we have unveiled the hidden properties of this circle. This journey helps us appreciate the connection between algebraic equations and geometric figures.