https://file.aiquickdraw.com/mathbot/file/1726640771201s37auxt8.jpg

The exercises in the image require identifying the correct graph for each circle equation. The general form of the circle equation is:

\[
(x - h)^2 + (y - k)^2 = r^2
\]

Where \((h, k)\) is the center of the circle and \(r\) is the radius.

### Equations and analysis:

5. \((x - 3)^2 + (y - 2)^2 = 64\)
   - Center: \((3, 2)\)
   - Radius: \(\sqrt{64} = 8\)

6. \((x - 3)^2 + (y + 2)^2 = 64\)
   - Center: \((3, -2)\)
   - Radius: \(8\)

7. \((x + 3)^2 + (y - 2)^2 = 64\)
   - Center: \((-3, 2)\)
   - Radius: \(8\)

8. \((x + 3)^2 + (y + 2)^2 = 64\)
   - Center: \((-3, -2)\)
   - Radius: \(8\)

### Graph Matching:

- **Graph 1**: Centered at \((3, 2)\), matches Equation 5.
- **Graph 2**: Centered at \((3, -2)\), matches Equation 6.
- **Graph 3**: Centered at \((-3, 2)\), matches Equation 7.
- **Graph 4**: Centered at \((-3, -2)\), matches Equation 8.

### Conclusion:

- Exercise 5 corresponds to Graph 1.
- Exercise 6 corresponds to Graph 2.
- Exercise 7 corresponds to Graph 3.
- Exercise 8 corresponds to Graph 4.

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Would you like further details on how these equations are derived or how to solve similar problems? Here are five questions for deeper exploration:

1. How do you derive the radius from the circle equation?
2. Can the equation of a circle be written in a different form?
3. What changes in the graph if we alter the radius of the circle?
4. How do translations affect the graph of a circle?
5. What is the significance of the center in graphing a circle?

**Tip:** Always identify the center and radius first to make graphing circles easier!

Complete exercises 5-8 by selecting the correct graph for each exercise: (x-3)^2 + (y-2)^2 = 64, (x-3)^2 + (y+2)^2 = 64, (x+3)^2 + (y-2)^2 = 64, (x+3)^2 + (y+2)^2 = 64. The graphs depict circles on a coordinate plane.

Match each circle equation with its correct graph. The exercises cover identifying the center and radius from equations in the form (x - h)^2 + (y - k)^2 = r^2. Suitable for Grades 9-10, this problem reinforces key geometry concepts on the coordinate plane.

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