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 (−3, −1), meaning the circle is located 3 units left and 1 unit down from the origin. Understanding the center's coordinates is crucial for accurately placing the circle on a coordinate plane.
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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 = √3, which indicates that the circle extends √3 units from its center in all directions. Knowing the radius is essential for determining the size of the circle and completing its equation.
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