Concept Check Match each equation in Column I with its graph in Column II. I II 47. (x - 3)² + (y - 2)² = 25 A. 48. B. 49. C. 50. D.

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Step 1: Recognize that the equation given, \((x - 3)^2 + (y - 2)^2 = 25\), represents a circle in the coordinate plane. This is because it is in the standard form of a circle's equation: \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius.

Step 2: Identify the center of the circle from the equation. Here, the center is at the point \((3, 2)\) because the equation is \((x - 3)^2 + (y - 2)^2 = 25\).

Step 3: Determine the radius of the circle by taking the square root of the right side of the equation. Since \(25\) is \(r^2\), the radius \(r\) is \(\sqrt{25}\).

Step 4: Use the center and radius information to match the equation to the correct graph in Column II. Look for the graph that shows a circle centered at \((3, 2)\) with radius equal to \(r\).

Step 5: Repeat this process for the other equations in Column I by identifying their forms (circle, ellipse, parabola, hyperbola, etc.) and matching their key features (center, vertices, axes lengths) to the graphs in Column II.

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