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 (0, 4), radius 4
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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 involves plotting its center on a coordinate plane and using the radius to determine the points that lie on the circle. From the center, you can move r units in all directions (up, down, left, right) to find key points, which helps in sketching the circle accurately.
Coordinate geometry is the study of geometric figures using a coordinate system, typically the Cartesian plane. It provides a framework for representing shapes like circles with equations, allowing for the analysis of their properties and relationships with other geometric figures.