Here are the essential concepts you must grasp in order to answer the question correctly.
Circle Equation
The equation (x + 3)² + (y - 2)² = 25 represents a circle in the Cartesian plane. The center of the circle is at the point (-3, 2), and the radius is the square root of 25, which is 5. Understanding this standard form of a circle's equation is crucial for identifying its graph.
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Graphing Techniques
Graphing techniques involve plotting points and understanding the shape of various equations. For circles, one must recognize that the graph will be a closed curve, symmetric about its center. Familiarity with how to translate the equation into a visual representation is essential for matching it with the correct graph.
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Coordinate Geometry
Coordinate geometry is the study of geometric figures using a coordinate system. It allows for the analysis of shapes like circles, lines, and parabolas in a two-dimensional space. Mastery of this concept helps in interpreting the relationships between algebraic equations and their graphical representations.
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