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.
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Graphing a Circle
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 mark key points, which helps in sketching the circular shape accurately.
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Distance Formula
The distance formula, derived from the Pythagorean theorem, calculates the distance between two points in a plane. It is given by d = √((x₂ - x₁)² + (y₂ - y₁)²). This concept is essential for understanding how far points are from the center of the circle, particularly when determining if a point lies on the circle.
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