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Grade 10–11Common Core (CCSS) · Math: geometry

Math · Grade 10

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The circle's equation · Grade 10

Name: ____________________

Worked example

  1. The circle x² + y² = r² has centre at the origin and radius r.
  2. The radius is the distance between centre (h, k) and a point (a, b): r = √((a − h)² + (b − k)²).
  3. Example: centre (0, 0) through (3, 4) gives r = √(9 + 16) = 5.
Example: how to solve it
1.

The circle x² + y² = 49. Find the radius.

2.

The circle x² + y² = 36. Find the radius.

3.

The circle x² + y² = 9. Find the radius.

4.

The circle x² + y² = 64. Find the radius.

5.

The circle x² + y² = 81. Find the radius.

6.

The circle x² + y² = 121. Find the radius.

7.

The circle x² + y² = 16. Find the radius.

8.

The circle x² + y² = 144. Find the radius.

9.

The circle x² + y² = 25. Find the radius.

10.

The circle x² + y² = 100. Find the radius.

11.

The circle x² + y² = 64. Find the radius.

12.

The circle x² + y² = 64. Find the radius.

13.

The circle x² + y² = 144. Find the radius.

14.

The circle x² + y² = 81. Find the radius.

15.

The circle x² + y² = 64. Find the radius.

16.

The circle x² + y² = 144. Find the radius.

17.

The circle x² + y² = 100. Find the radius.

18.

The circle x² + y² = 64. Find the radius.

19.

The circle x² + y² = 64. Find the radius.

20.

The circle x² + y² = 25. Find the radius.

Answer key

  1. 1. r = 7
  2. 2. r = 6
  3. 3. r = 3
  4. 4. r = 8
  5. 5. r = 9
  6. 6. r = 11
  7. 7. r = 4
  8. 8. r = 12
  9. 9. r = 5
  10. 10. r = 10
  11. 11. r = 8
  12. 12. r = 8
  13. 13. r = 12
  14. 14. r = 9
  15. 15. r = 8
  16. 16. r = 12
  17. 17. r = 10
  18. 18. r = 8
  19. 19. r = 8
  20. 20. r = 5

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Area
Geometry
Exercise type
The circle's equation
Grade
10 (ages 15–16)
Difficulty
Easy
Number of tasks
20
Task format
Calculations
Paper size
US Letter
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Area
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Practise the equation of a circle and the radius as the distance between centre and point.

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Easy reads the radius from x² + y² = r², medium and hard use the distance formula — always with whole-number answers. The answer key is calculated by the website. No sign-up needed.

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