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Write the equation of a circle from its centre and radius

10th grade (Year 11 in England) · 16 questions · Common Core: HSG.GPE.A.1 · England: GCSE Higher Algebra

Name

Date

Score/ 16

  1. Question 1

    Which is the equation of the circle with centre (−2, 6) and radius 6?

    • A. (x + 2)² + (y − 6)² = 6
    • B. (x − 6)² + (y + 2)² = 36
    • C. (x − 2)² + (y + 6)² = 36
    • D. (x + 2)² + (y − 6)² = 36

  2. Question 2

    A circle has centre (4, −3) and passes through (−1, 0). Its equation is (x − 4)² + (y + 3)² = k. Find k.

    Answer

  3. Question 3

    Where is the point (−4, −3) relative to the circle (x − 3)² + y² = 49?

    • A. Inside the circle
    • B. On the circle
    • C. Outside the circle

  4. Question 4

    Which is the equation of the circle with centre (2, −5) and radius 6?

    • A. (x + 2)² + (y − 5)² = 6
    • B. (x + 2)² + (y − 5)² = 36
    • C. (x − 2)² + (y + 5)² = 36
    • D. (x + 5)² + (y − 2)² = 36

  5. Question 5

    A circle has centre (−1, −3) and passes through (−1, 5). Its equation is (x + 1)² + (y + 3)² = k. Find k.

    Answer

  6. Question 6

    Where is the point (−9, −4) relative to the circle (x − 1)² + (y + 4)² = 100?

    • A. Inside the circle
    • B. On the circle
    • C. Outside the circle

  7. Question 7

    Which is the equation of the circle with centre (−1, −1) and radius 4?

    • A. (x − 1)² + (y − 1)² = 4
    • B. (x + 1)² + (y + 1)² = 16
    • C. (x − 1)² + (y − 1)² = 16
    • D. (x + 1)² + (y + 1)² = 4

  8. Question 8

    A circle has centre (−4, 4) and passes through (6, −1). Its equation is (x + 4)² + (y − 4)² = k. Find k.

    Answer

  9. Question 9

    Where is the point (4, 4) relative to the circle (x − 3)² + (y − 4)² = 4?

    • A. Inside the circle
    • B. On the circle
    • C. Outside the circle

  10. Question 10

    Which is the equation of the circle with centre (4, −3) and radius 6?

    • A. (x − 4)² + (y + 3)² = 36
    • B. (x + 4)² + (y − 3)² = 36
    • C. (x + 3)² + (y − 4)² = 36
    • D. (x + 4)² + (y − 3)² = 6

  11. Question 11

    A circle has centre (−3, 4) and passes through (2, 2). Its equation is (x + 3)² + (y − 4)² = k. Find k.

    Answer

  12. Question 12

    Where is the point (−10, −3) relative to the circle (x + 4)² + (y + 3)² = 36?

    • A. Inside the circle
    • B. On the circle
    • C. Outside the circle

  13. Question 13

    Which is the equation of the circle with centre (−6, −1) and radius 4?

    • A. (x + 6)² + (y + 1)² = 16
    • B. (x + 1)² + (y + 6)² = 16
    • C. (x − 6)² + (y − 1)² = 4
    • D. (x + 6)² + (y + 1)² = 4

  14. Question 14

    A circle has centre (5, −4) and passes through (4, 3). Its equation is (x − 5)² + (y + 4)² = k. Find k.

    Answer

  15. Question 15

    Where is the point (−2, −4) relative to the circle (x + 2)² + (y + 2)² = 4?

    • A. Inside the circle
    • B. On the circle
    • C. Outside the circle

  16. Question 16

    Which is the equation of the circle with centre (1, 5) and radius 4?

    • A. (x + 1)² + (y + 5)² = 4
    • B. (x − 5)² + (y − 1)² = 16
    • C. (x − 1)² + (y − 5)² = 16
    • D. (x + 1)² + (y + 5)² = 16

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  1. (x + 2)² + (y − 6)² = 36
  2. 34
  3. Outside the circle
  4. (x − 2)² + (y + 5)² = 36
  5. 64
  6. On the circle
  7. (x + 1)² + (y + 1)² = 16
  8. 125
  9. Inside the circle
  10. (x − 4)² + (y + 3)² = 36
  11. 29
  12. On the circle
  13. (x + 6)² + (y + 1)² = 16
  14. 50
  15. On the circle
  16. (x − 1)² + (y − 5)² = 16