Question

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.

Accepted Answer

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.

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.

Verified video answer for a similar problem:

Key Concepts

Equation of a Circle

Graph Interpretation

Coordinate Geometry Basics