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 (-2, 4), meaning the circle is positioned 2 units left and 4 units up from the origin on the Cartesian plane. Understanding the center's coordinates is crucial for accurately writing the 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. In this problem, the radius is given as r = 6, which means that every point on the circle is 6 units away from the center. This value is essential for determining the right side of the standard form equation.
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