In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 1 and 2. center (2, 0), radius 6

Key Concepts

Center-Radius Form of a Circle

The center-radius form of a circle's equation is expressed as (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. This format allows for easy identification of the circle's center and radius, facilitating both graphing and analysis.

Graphing a Circle

Graphing a circle involves plotting the center point on a coordinate plane and then using the radius to determine the circle's boundary. From the center, you can measure the radius in all directions to mark points that define the circle, which is then drawn as a smooth curve connecting these points.

Coordinate Geometry

Coordinate geometry, or analytic geometry, is the study of geometric figures using a coordinate system. It combines algebra and geometry, allowing for the representation of shapes like circles, lines, and polygons in a two-dimensional space, which is essential for solving problems involving their equations and graphs.