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Circles as Conics - Worksheet 8 - 11th Grade

Hard

Read standard-form conic equations to identify centers, vertices, dimensions and curve types.

hard: Use another set to practice explaining and checking your answers.

27 problems · 20-25 minutes · Skills: conic sections, circles, graphing

About This Worksheet

This hard-level worksheet contains 27 problems designed for 11th Grade students practicing circles as conics. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.

Factor polynomials, use exponent laws and solve equations with domain restrictions.

  • Read standard-form conic equations to identify centers, vertices, dimensions and curve types.
  • Check your result using the method in the example before moving to the next question.

How to Solve: Worked Example

Example Problem: Find the center and radius of (x + 1)² + (y - 3)² = 4.
Solution Steps:
  1. Compare with (x − h)² + (y − k)² = r².
  2. Take the positive square root of r².
Answer: Center (-1, 3); radius 2.
Tip: Check your result using the method in the example before moving to the next question.
1
Find the center and radius of (x + 3)² + (y + 5)² = 4.
2
Find the center and radius of (x - 5)² + (y - 2)² = 16.
3
Find the center and radius of (x - 3)² + (y - 5)² = 9.
4
Find the center and radius of (x + 5)² + (y + 1)² = 4.
5
Find the center and radius of (x + 1)² + (y + 0)² = 25.
6
Find the center and radius of (x + 3)² + (y - 5)² = 9.
7
Find the center and radius of (x - 3)² + (y - 3)² = 1.
8
Find the center and radius of (x + 5)² + (y - 3)² = 25.
9
Find the center and radius of (x - 5)² + (y - 3)² = 16.
10
Find the center and radius of (x - 3)² + (y - 5)² = 1.
11
Find the center and radius of (x + 5)² + (y + 3)² = 1.
12
Find the center and radius of (x + 3)² + (y + 4)² = 1.
13
Find the center and radius of (x + 0)² + (y - 3)² = 1.
14
Find the center and radius of (x - 3)² + (y + 5)² = 4.
15
Find the center and radius of (x + 5)² + (y + 3)² = 25.
16
Find the center and radius of (x + 4)² + (y + 3)² = 4.
17
Find the center and radius of (x - 2)² + (y + 2)² = 16.
18
Find the center and radius of (x + 5)² + (y + 2)² = 16.
19
Find the center and radius of (x + 1)² + (y - 4)² = 1.
20
Find the center and radius of (x - 5)² + (y + 0)² = 16.
21
Find the center and radius of (x + 2)² + (y + 2)² = 1.
22
Find the center and radius of (x - 2)² + (y + 5)² = 9.
23
Find the center and radius of (x + 4)² + (y - 1)² = 9.
24
Find the center and radius of (x + 0)² + (y + 4)² = 25.
25
Find the center and radius of (x + 1)² + (y - 2)² = 1.
26
Find the center and radius of (x - 5)² + (y + 0)² = 25.
27
Find the center and radius of (x + 4)² + (y + 1)² = 9.

Answer Key

1. Center (-3, -5); radius 2.2. Center (5, 2); radius 4.3. Center (3, 5); radius 3.4. Center (-5, -1); radius 2.5. Center (-1, 0); radius 5.6. Center (-3, 5); radius 3.7. Center (3, 3); radius 1.8. Center (-5, 3); radius 5.9. Center (5, 3); radius 4.10. Center (3, 5); radius 1.11. Center (-5, -3); radius 1.12. Center (-3, -4); radius 1.13. Center (0, 3); radius 1.14. Center (3, -5); radius 2.15. Center (-5, -3); radius 5.16. Center (-4, -3); radius 2.17. Center (2, -2); radius 4.18. Center (-5, -2); radius 4.19. Center (-1, 4); radius 1.20. Center (5, 0); radius 4.21. Center (-2, -2); radius 1.22. Center (2, -5); radius 3.23. Center (-4, 1); radius 3.24. Center (0, -4); radius 5.25. Center (-1, 2); radius 1.26. Center (5, 0); radius 5.27. Center (-4, -1); radius 3.

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What skills does this conic sections worksheet cover?

This worksheet focuses on conic sections, circles, graphing. It is designed for 11th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

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How many problems are on this worksheet?

This worksheet contains 27 problems. It typically takes 20-25 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.