✏️ Equations of Circles: Practice A (G-GPE.A.1)

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Derive the equation of a circle; find center and radius by completing the square. Solve each problem.

1. Equation of a circle, center (-1, 4), radius 5

2. x² + y² + 16x + 8y − 1 = 0. Center and radius?

3. Equation of a circle, center (3, 0), radius 6

4. x² + y² + 16x + 10y + 25 = 0. Center and radius?

5. Equation of a circle, center (2, -4), radius 3

6. x² + y² + 10x + 8y + 37 = 0. Center and radius?

7. Equation of a circle, center (6, 2), radius 8

8. x² + y²x + 6y + 5 = 0. Center and radius?

9. Equation of a circle, center (-5, 7), radius 9

10. x² + y²x − 8y − 65 = 0. Center and radius?

11. Equation of a circle, center (0, 7), radius 4

12. x² + y² + 10x − 14y + 25 = 0. Center and radius?

Answer key: 1) (x + 1)² + (y − 4)² = 25 · 2) center (-8, -4), r = 9 · 3) (x − 3)² + (y)² = 36 · 4) center (-8, -5), r = 8 · 5) (x − 2)² + (y + 4)² = 9 · 6) center (-5, -4), r = 2 · 7) (x − 6)² + (y − 2)² = 64 · 8) center (0, -3), r = 2 · 9) (x + 5)² + (y − 7)² = 81 · 10) center (0, 4), r = 9 · 11) (x)² + (y − 7)² = 16 · 12) center (-5, 7), r = 7

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Worksheets › Grade 10 Math (Geometry) › Equations of Circles › Equations of Circles

Grade 10 (ages 15–16)Numbers & mathsFree printable PDF

About this grade 10 worksheet

Free Grade 10 Geometry math worksheet (Common Core G-GPE.A.1): equations of circles — twelve practice problems, with answer key. Skill: Derive the equation of a circle; find center and radius by completing the square. Level: Grade 10 — also suits Year 11 (UK).

For teachers: skills & standards

CCSS G-GPE.A.1: Derive the equation of a circle; find center and radius by completing the square
Works as a morning-work page, a centre/station activity, homework or an early-finisher task.

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It is designed for Grade 10 (ages 15–16), but use it with any child who is ready.

What skills does it build?

Derive the equation of a circle; find center and radius by completing the square.

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More “Equations of Circles” printables (g-gpe.a.1: derive the equation of a circle; find center and radius by completing the square)

Equations of Circles: Practice B (G-GPE.A.1) · Equations of Circles: Mixed Practice & Reasoning (G-GPE.A.1) · Equations of Circles: Show Your Thinking (G-GPE.A.1) · Equations of Circles: Quick Check (G-GPE.A.1)

All 5 equations of circles sheets → · Grade 10 Math (Geometry): all 10 skills → · All Common Core grades

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