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Grade 10 Equations of Circles Worksheet with Answers

Grade 10 (US) · Year 11 (UK) · Class 10 (India) · Math

Unit 1: Coordinate GeometryCircles on the Coordinate PlaneCCSS G-GPE.A.1

Writing and reading the center-radius equation of a circle. This free high school worksheet has 12 questions and a full answer key. Print it or save it as a PDF — every answer is checked by code, not guessed.

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Equations of Circles

Grade 10 · Math

Score___ / 12

Name

Class

Date

Learning goal: Circles on the Coordinate Plane · CCSS G-GPE.A.1

Directions: Use the pictures to help you. Solve each problem. Show your work, then write your answer in the box.

Example

What is the center of the circle (x + 5)^2 + (y - 6)^2 = 16?

Answer: (-5, 6)

RememberCircles

rdRadius r: centre to edgeDiameter d = 2rCircumference C = 2πr = πdArea A = πr²Sector = (angle ÷ 360) × πr²
  1. 1

    What is the radius of the circle (x - 7)^2 + (y - 5)^2 = 100?

    Answer
  2. 2

    Write the equation of the circle with center (1, 3) and radius 5.

    r = 5
    Answer
  3. 3

    What is the radius of the circle (x + 3)^2 + (y - 7)^2 = 1?

    Answer
  4. 4

    Write the equation of the circle with center (-8, 5) and radius 1.

    r = 1
    Answer
  5. 5

    What is the radius of the circle (x - 3)^2 + (y - 5)^2 = 1?

    Answer
  6. 6

    Write the equation of the circle with center (-4, 2) and radius 8.

    Answer
  7. 7

    Write the equation of the circle with center (8, -2) and radius 4.

    Answer
  8. 8

    Write the equation of the circle with center (8, 7) and radius 9.

    Answer
  9. 9

    Write the equation of the circle with center (-4, 5) and radius 9.

    Answer
  10. 10

    Write the equation of the circle with center (-3, 7) and radius 10.

    Answer
  11. 11

    Write the equation of the circle with center (3, 1) and radius 6.

    r = 6
    Answer
  12. 12

    What is the center of the circle (x + 3)^2 + (y - 1)^2 = 9?

    Answer

★ Challenge corner for fast finishers

You have 2 shirts, 4 pairs of pants and 3 hats. How many different outfits of one shirt, one pair of pants and one hat can you make?

How did I do?

Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/10/circle_equation

Answer key (click to show)
  1. 1.10
  2. 2.(x - 1)^2 + (y - 3)^2 = 25
  3. 3.1
  4. 4.(x + 8)^2 + (y - 5)^2 = 1
  5. 5.1
  6. 6.(x + 4)^2 + (y - 2)^2 = 64
  7. 7.(x - 8)^2 + (y + 2)^2 = 16
  8. 8.(x - 8)^2 + (y - 7)^2 = 81
  9. 9.(x + 4)^2 + (y - 5)^2 = 81
  10. 10.(x + 3)^2 + (y - 7)^2 = 100
  11. 11.(x - 3)^2 + (y - 1)^2 = 36
  12. 12.(-3, 1)
  13. ★24 (challenge corner)

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