Looking at this worksheet, I need to match each circle equation with its corresponding graph.
Let me start by recalling the standard form of a circle equation:
(x - h)² + (y - k)² = r²
Where:
- (h, k) is the center of the circle
- r is the radius
Now let me analyze each equation one by one:
1. (x - 2)² + (y + 1)² = 16
- Center: (2, -1)
- Radius: √16 = 4
- This should be a circle centered at (2, -1) with radius 4
2. (x + 4)² + (y - 1)² = 36
- Center: (-4, 1)
- Radius: √36 = 6
- This should be a circle centered at (-4, 1) with radius 6
3. (x + 2)² + (y + 4)² = 25
- Center: (-2, -4)
- Radius: √25 = 5
- This should be a circle centered at (-2, -4) with radius 5
4. (x² + y²) = 100/25 = 4
- Wait, let me recalculate: 100/25 = 4
- So: x² + y² = 4
- Center: (0, 0)
- Radius: √4 = 2
- This should be a circle centered at origin with radius 2
5. (x - 3)² + (y - 3)² = 36
- Center: (3, 3)
- Radius: √36 = 6
- This should be a circle centered at (3, 3) with radius 6
6. (x + 3)² + (y + 4)² = 49
- Center: (-3, -4)
- Radius: √49 = 7
- This should be a circle centered at (-3, -4) with radius 7
7. (x - 1)² + (y - 2)² = 2
- Center: (1, 2)
- Radius: √2 ≈ 1.41
- This should be a small circle centered at (1, 2)
8. (x - 4)² + (y - 1)² = 9/25
- Center: (4, 1)
- Radius: √(9/25) = 3/5 = 0.6
- This should be a very small circle centered at (4, 1)
9. (x - 4)² + (y - 1)² = 25
- Center: (4, 1)
- Radius: √25 = 5
- This should be a circle centered at (4, 1) with radius 5
10. (x - 1)² + (y + 1)² = 4
- Center: (1, -1)
- Radius: √4 = 2
- This should be a circle centered at (1, -1) with radius 2
Now let me match these with the graphs:
Looking at the graphs:
- Graph 1: Circle centered at approximately (2, -1) with radius 4 → matches equation 1
- Graph 2: Circle centered at approximately (-4, 1) with radius 6 → matches equation 2
- Graph 3: Circle centered at approximately (-2, -4) with radius 5 → matches equation 3
- Graph 4: Circle centered at origin with radius 2 → matches equation 4
- Graph 5: Circle centered at approximately (3, 3) with radius 6 → matches equation 5
- Graph 6: Circle centered at approximately (-3, -4) with radius 7 → matches equation 6
- Graph 7: Small circle centered at approximately (1, 2) → matches equation 7
- Graph 8: Very small circle centered at approximately (4, 1) → matches equation 8
- Graph 9: Circle centered at approximately (4, 1) with radius 5 → matches equation 9
- Graph 10: Circle centered at approximately (1, -1) with radius 2 → matches equation 10
The matching is straightforward - each equation corresponds to the graph with the same number.
Final Answer:
1-A, 2-B, 3-C, 4-D, 5-E, 6-F, 7-G, 8-H, 9-I, 10-J
Parent Tip: Review the logic above to help your child master the concept of equation of a circle worksheet.
