Worksheet

Read and write the equation of a circle

Grade 10 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

  1. Ari draws a drum top on a grid: its center is C(1, 2), and it passes through Q(4, 6). Which equation is the circle?

    • (x − 1)² + (y − 2)² = 49
    • (x − 1)² + (y − 2)² = 5
    • (x + 1)² + (y + 2)² = 25
    • (x − 1)² + (y − 2)² = 25

  2. Bo draws a round flower bed in a park on a grid: its center is C(-2, 3), and it passes through Q(4, 11). Which equation is the circle?

    • (x + 2)² + (y − 3)² = 10
    • (x − 2)² + (y + 3)² = 100
    • (x + 2)² + (y − 3)² = 100
    • (x + 2)² + (y − 3)² = 196

  3. Esme draws a bike wheel on a grid: its center is C(3, -1), and it passes through Q(8, 11). Which equation is the circle?

    • (x + 3)² + (y − 1)² = 169
    • (x − 3)² + (y + 1)² = 13
    • (x − 3)² + (y + 1)² = 169
    • (x − 3)² + (y + 1)² = 289

  4. Jun draws a round cake on a grid: its center is C(-4, -4), and it passes through Q(-1, 0). Which equation is the circle?

    • (x − 4)² + (y − 4)² = 25
    • (x + 4)² + (y + 4)² = 5
    • (x + 4)² + (y + 4)² = 25
    • (x + 4)² + (y + 4)² = 49

  5. Read this first

    Grid

    The circle and the point Q.

  6. Luz draws a round pizza on a grid as (x + 3)² + (y − 2)² = 25. Is the point Q(-5, 1) on the circle, inside it or outside it?

    • outside the circle
    • on the circle
    • inside the circle

  7. Milo draws a round pond on a grid as (x − 1)² + (y − 4)² = 25. Is the point Q(-6, -4) on the circle, inside it or outside it?

    • on the circle
    • inside the circle
    • outside the circle

  8. Noah draws a sun shape in a mural on a grid as (x + 2)² + (y + 3)² = 25. Is the point Q(-4, -4) on the circle, inside it or outside it?

    • inside the circle
    • outside the circle
    • on the circle

  9. a circle with center C(1, -2); a radius is drawn as the long side of a right triangle under it. Pia draws a drum top on a grid as (x − 1)² + (y + 2)² = 18. Give an exact answer, simplified. How long is the radius?

  10. a circle with center C(-3, 4); a radius is drawn as the long side of a right triangle under it. Ren draws a round flower bed in a park on a grid as (x + 3)² + (y − 4)² = 50. Give an exact answer, simplified. How long is the radius?

  11. a circle with center C(-4, -1); a radius is drawn as the long side of a right triangle under it. Zee draws a round cake on a grid as (x + 4)² + (y + 1)² = 75. Give an exact answer, simplified. How long is the radius?

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Read and write the equation of a circle

Answer Key - Grade 10 Math Worksheet

Circle the best answer, or write your answer on the line.

  1. Ari draws a drum top on a grid: its center is C(1, 2), and it passes through Q(4, 6). Which equation is the circle?

    • (x − 1)² + (y − 2)² = 49
    • (x − 1)² + (y − 2)² = 5
    • (x + 1)² + (y + 2)² = 25
    • (x − 1)² + (y − 2)² = 25

  2. Bo draws a round flower bed in a park on a grid: its center is C(-2, 3), and it passes through Q(4, 11). Which equation is the circle?

    • (x + 2)² + (y − 3)² = 10
    • (x − 2)² + (y + 3)² = 100
    • (x + 2)² + (y − 3)² = 100
    • (x + 2)² + (y − 3)² = 196

  3. Esme draws a bike wheel on a grid: its center is C(3, -1), and it passes through Q(8, 11). Which equation is the circle?

    • (x + 3)² + (y − 1)² = 169
    • (x − 3)² + (y + 1)² = 13
    • (x − 3)² + (y + 1)² = 169
    • (x − 3)² + (y + 1)² = 289

  4. Jun draws a round cake on a grid: its center is C(-4, -4), and it passes through Q(-1, 0). Which equation is the circle?

    • (x − 4)² + (y − 4)² = 25
    • (x + 4)² + (y + 4)² = 5
    • (x + 4)² + (y + 4)² = 25
    • (x + 4)² + (y + 4)² = 49

  5. Read this first

    Grid

    The circle and the point Q.

  6. Luz draws a round pizza on a grid as (x + 3)² + (y − 2)² = 25. Is the point Q(-5, 1) on the circle, inside it or outside it?

    • outside the circle
    • on the circle
    • inside the circle

  7. Milo draws a round pond on a grid as (x − 1)² + (y − 4)² = 25. Is the point Q(-6, -4) on the circle, inside it or outside it?

    • on the circle
    • inside the circle
    • outside the circle

  8. Noah draws a sun shape in a mural on a grid as (x + 2)² + (y + 3)² = 25. Is the point Q(-4, -4) on the circle, inside it or outside it?

    • inside the circle
    • outside the circle
    • on the circle

  9. a circle with center C(1, -2); a radius is drawn as the long side of a right triangle under it. Pia draws a drum top on a grid as (x − 1)² + (y + 2)² = 18. Give an exact answer, simplified. How long is the radius?

    3√2

  10. a circle with center C(-3, 4); a radius is drawn as the long side of a right triangle under it. Ren draws a round flower bed in a park on a grid as (x + 3)² + (y − 4)² = 50. Give an exact answer, simplified. How long is the radius?

    5√2

  11. a circle with center C(-4, -1); a radius is drawn as the long side of a right triangle under it. Zee draws a round cake on a grid as (x + 4)² + (y + 1)² = 75. Give an exact answer, simplified. How long is the radius?

    5√3