## Exploring the Circle: (x-1)^2 + y^2 = 1

The equation **(x-1)^2 + y^2 = 1** represents a circle in the standard form of a circle equation. Let's delve into its properties and understand how it's derived.

### Standard Form of a Circle Equation

The general standard form of a circle equation 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.

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

In our equation **(x-1)^2 + y^2 = 1**, we can identify the following:

**Center:**(1, 0)**Radius:**1

This tells us that the circle is centered at the point (1, 0) and has a radius of 1 unit.

### Visualizing the Circle

To visualize this circle, we can plot points on a graph:

**Center:**Mark the point (1, 0) as the center of the circle.**Radius:**From the center, move 1 unit in all directions (up, down, left, right) and mark these points.**Connect the Points:**Connect these points smoothly to form the circle.

This will create a circle with a radius of 1 unit, centered at the point (1, 0).

### Key Takeaways

- The equation
**(x-1)^2 + y^2 = 1**represents a circle with a center at (1, 0) and a radius of 1 unit. - The standard form of the circle equation makes it easy to identify the center and radius.
- Visualizing the circle by plotting points helps understand the geometric representation of the equation.

This equation serves as a simple yet powerful example to demonstrate the relationship between algebraic equations and geometric shapes, making it a valuable tool in various mathematical applications.