(x-1)^2+y^2=1

Jasonbradley

3 min read

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Jun 17, 2024

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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:

1. Center: Mark the point (1, 0) as the center of the circle.
2. Radius: From the center, move 1 unit in all directions (up, down, left, right) and mark these points.
3. 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.