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Find the centre and radius from x² + y² + Dx + Ey + F = 0

10th grade (Year 11 in England) · 16 questions · Common Core: HSG.GPE.A.1 · England: A-level Pure Mathematics

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Date

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  1. Question 1

    Find the radius of the circle x² + y² − 2x + 8y + 8 = 0.

    Answer

  2. Question 2

    Find the centre of the circle x² + y² − 2x − 4y − 59 = 0. Type it like (2, −1).

    Answer

  3. Question 3

    Find the radius of the circle x² + y² + 2x − 4y − 4 = 0.

    Answer

  4. Question 4

    Find the centre of the circle x² + y² − 4x + 2y − 20 = 0. Type it like (2, −1).

    Answer

  5. Question 5

    Find the radius of the circle x² + y² + 6x − 8y + 21 = 0.

    Answer

  6. Question 6

    Find the centre of the circle x² + y² − 4x + 8y − 5 = 0. Type it like (2, −1).

    Answer

  7. Question 7

    Find the radius of the circle x² + y² − 10x + 4y + 13 = 0.

    Answer

  8. Question 8

    Find the centre of the circle x² + y² − 2x + 10y + 25 = 0. Type it like (2, −1).

    Answer

  9. Question 9

    Find the radius of the circle x² + y² + 6x − 6y + 9 = 0.

    Answer

  10. Question 10

    Find the centre of the circle x² + y² − 2x + 10y + 1 = 0. Type it like (2, −1).

    Answer

  11. Question 11

    Find the radius of the circle x² + y² + 12x + 12y − 9 = 0.

    Answer

  12. Question 12

    Find the centre of the circle x² + y² + 4x + 2y − 76 = 0. Type it like (2, −1).

    Answer

  13. Question 13

    Find the radius of the circle x² + y² + 8x + 6y − 39 = 0.

    Answer

  14. Question 14

    Find the centre of the circle x² + y² − 12x − 6y + 41 = 0. Type it like (2, −1).

    Answer

  15. Question 15

    Find the radius of the circle x² + y² + 8x − 6y + 24 = 0.

    Answer

  16. Question 16

    Find the centre of the circle x² + y² + 2x − 6y − 54 = 0. Type it like (2, −1).

    Answer

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Answer key: Find the centre and radius from x² + y² + Dx + Ey + F = 0

  1. 1. 3

  2. 2. (1, 2)

  3. 3. 3

  4. 4. (2, −1)

  5. 5. 2

  6. 6. (2, −4)

  7. 7. 4

  8. 8. (1, −5)

  9. 9. 3

  10. 10. (1, −5)

  11. 11. 9

  12. 12. (−2, −1)

  13. 13. 8

  14. 14. (6, 3)

  15. 15. 1

  16. 16. (−1, 3)