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 (5, -4), radius 7

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 its center on a coordinate plane and using the radius to determine the circle's boundary. From the center, you can measure the radius in all directions to mark points on the circle, which helps visualize its shape and size.

Coordinate Geometry

Coordinate geometry, or analytic geometry, involves using a coordinate system to represent geometric shapes and their properties. Understanding how to manipulate and interpret coordinates is essential for solving problems related to circles, including finding their equations and graphing them accurately.