Worksheet

Circles in general form: complete the square and graph

Grade 10 Math Worksheet - Challenge Me

NameDate

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

  2. Milo writes the edge of a bike wheel as 2x² + 2y² − 8x + 12y − 6 = 0. Which equation is the circle in standard form?

    • (x − 2)² + (y + 3)² = 16
    • (x − 4)² + (y + 6)² = 58
    • (x + 2)² + (y − 3)² = 16
    • (x − 2)² + (y + 3)² = 4

  3. Noah writes the edge of a cake as 3x² + 3y² + 12x − 6y − 33 = 0. Which equation is the circle in standard form?

    Use the picture in question 1.

    • (x + 6)² + (y − 3)² = 78
    • (x + 2)² + (y − 1)² = 4
    • (x − 2)² + (y + 1)² = 16
    • (x + 2)² + (y − 1)² = 16

  4. Pia writes the edge of a sun in a mural as 4x² + 4y² − 16x − 8y − 16 = 0. Which equation is the circle in standard form?

    Use the picture in question 1.

    • (x − 8)² + (y − 4)² = 96
    • (x − 2)² + (y − 1)² = 9
    • (x + 2)² + (y + 1)² = 9
    • (x − 2)² + (y − 1)² = 3

  5. Ren writes the edge of a round flower bed as 2x² + 2y² + 4x + 16y + 2 = 0. Which equation is the circle in standard form?

    Use the picture in question 1.

    • (x − 1)² + (y − 4)² = 16
    • (x + 2)² + (y + 8)² = 66
    • (x + 1)² + (y + 4)² = 4
    • (x + 1)² + (y + 4)² = 16

  6. Zee checks the equation x² + y² + 2x − 4y + 9 = 0 before drawing a pizza. What is its graph?

    Use the picture in question 1.

    • a circle with radius √14
    • a circle with radius 4
    • no graph at all
    • a single point

  7. Ari checks the equation x² + y² − 6x − 8y + 9 = 0 before drawing a pond. What is its graph?

    Use the picture in question 1.

    • a circle with radius 4
    • no graph at all
    • a circle with radius √34
    • a single point

  8. Esme writes the edge of a bike wheel as x² + y² − 4x + 2y − 3 = 0. Give an exact answer, simplified. How long is the radius?

    Use the picture in question 1.

  9. Jun writes the edge of a cake as x² + y² + 6x − 6y − 2 = 0. Give an exact answer, simplified. How long is the radius?

    Use the picture in question 1.

  10. Kira writes the edge of a sun in a mural as x² + y² − 2x − 10y + 8 = 0. Give an exact answer, simplified. How long is the radius?

    Use the picture in question 1.

  11. Luz writes the edge of a round flower bed as x² + y² + 8x + 4y + 8 = 0. Give an exact answer, simplified. How long is the radius?

    Use the picture in question 1.

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Circles in general form: complete the square and graph

Answer Key - Grade 10 Math Worksheet - Challenge Me

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

  2. Milo writes the edge of a bike wheel as 2x² + 2y² − 8x + 12y − 6 = 0. Which equation is the circle in standard form?

    • (x − 2)² + (y + 3)² = 16
    • (x − 4)² + (y + 6)² = 58
    • (x + 2)² + (y − 3)² = 16
    • (x − 2)² + (y + 3)² = 4

  3. Noah writes the edge of a cake as 3x² + 3y² + 12x − 6y − 33 = 0. Which equation is the circle in standard form?

    Use the picture in question 1.

    • (x + 6)² + (y − 3)² = 78
    • (x + 2)² + (y − 1)² = 4
    • (x − 2)² + (y + 1)² = 16
    • (x + 2)² + (y − 1)² = 16

  4. Pia writes the edge of a sun in a mural as 4x² + 4y² − 16x − 8y − 16 = 0. Which equation is the circle in standard form?

    Use the picture in question 1.

    • (x − 8)² + (y − 4)² = 96
    • (x − 2)² + (y − 1)² = 9
    • (x + 2)² + (y + 1)² = 9
    • (x − 2)² + (y − 1)² = 3

  5. Ren writes the edge of a round flower bed as 2x² + 2y² + 4x + 16y + 2 = 0. Which equation is the circle in standard form?

    Use the picture in question 1.

    • (x − 1)² + (y − 4)² = 16
    • (x + 2)² + (y + 8)² = 66
    • (x + 1)² + (y + 4)² = 4
    • (x + 1)² + (y + 4)² = 16

  6. Zee checks the equation x² + y² + 2x − 4y + 9 = 0 before drawing a pizza. What is its graph?

    Use the picture in question 1.

    • a circle with radius √14
    • a circle with radius 4
    • no graph at all
    • a single point

  7. Ari checks the equation x² + y² − 6x − 8y + 9 = 0 before drawing a pond. What is its graph?

    Use the picture in question 1.

    • a circle with radius 4
    • no graph at all
    • a circle with radius √34
    • a single point

  8. Esme writes the edge of a bike wheel as x² + y² − 4x + 2y − 3 = 0. Give an exact answer, simplified. How long is the radius?

    Use the picture in question 1.

    2√2

  9. Jun writes the edge of a cake as x² + y² + 6x − 6y − 2 = 0. Give an exact answer, simplified. How long is the radius?

    Use the picture in question 1.

    2√5

  10. Kira writes the edge of a sun in a mural as x² + y² − 2x − 10y + 8 = 0. Give an exact answer, simplified. How long is the radius?

    Use the picture in question 1.

    3√2

  11. Luz writes the edge of a round flower bed as x² + y² + 8x + 4y + 8 = 0. Give an exact answer, simplified. How long is the radius?

    Use the picture in question 1.

    2√3