Here are the essential concepts you must grasp in order to answer the question correctly.
Standard Form of a Circle's Equation
The standard form of a circle's equation is given by (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 graphing and analysis.
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Coordinates of the Center
The center of a circle is represented by the coordinates (h, k). In this case, the center is given as (-2, 4), meaning the circle is centered at the point where x = -2 and y = 4 on the Cartesian plane. Understanding the center's coordinates is crucial for correctly applying them in the standard form equation.
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Graphs & the Rectangular Coordinate System
Radius of a Circle
The radius of a circle is the distance from the center to any point on the circle. It is denoted by r and is a critical component in the standard form equation. In this problem, the radius is given as 6, which means that the circle extends 6 units from the center in all directions.
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