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
Question 1
Where is the point (9, −1) relative to the circle (x − 5)² + (y + 4)² = 36?
- A. Inside the circle
- B. On the circle
- C. Outside the circle
Question 2
Which is the equation of the circle with centre (−5, −1) and radius 3?
- A. (x − 5)² + (y − 1)² = 9
- B. (x + 5)² + (y + 1)² = 3
- C. (x + 5)² + (y + 1)² = 9
- D. (x − 5)² + (y − 1)² = 3
Question 3
A circle has centre (−1, 3) and passes through (5, −5). Its equation is (x + 1)² + (y − 3)² = k. Find k.
Answer
Question 4
Where is the point (2, −1) relative to the circle (x − 2)² + (y + 1)² = 4?
- A. Inside the circle
- B. On the circle
- C. Outside the circle
Question 5
Which is the equation of the circle with centre (5, 2) and radius 8?
- A. (x + 5)² + (y + 2)² = 8
- B. (x − 5)² + (y − 2)² = 64
- C. (x − 5)² + (y − 2)² = 8
- D. (x − 2)² + (y − 5)² = 64
Question 6
A circle has centre (−3, −5) and passes through (0, −4). Its equation is (x + 3)² + (y + 5)² = k. Find k.
Answer
Question 7
Where is the point (2, −2) relative to the circle (x − 3)² + (y + 2)² = 4?
- A. Inside the circle
- B. On the circle
- C. Outside the circle
Question 8
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 = 4
- C. (x + 1)² + (y − 1)² = 16
- D. (x − 1)² + (y + 1)² = 16
Question 9
A circle has centre (−1, 0) and passes through (−1, 3). Its equation is (x + 1)² + y² = k. Find k.
Answer
Question 10
Where is the point (13, −2) relative to the circle (x − 5)² + (y + 2)² = 64?
- A. Inside the circle
- B. On the circle
- C. Outside the circle
Question 11
Which is the equation of the circle with centre (−1, 6) and radius 3?
- A. (x − 1)² + (y + 6)² = 3
- B. (x − 1)² + (y + 6)² = 9
- C. (x + 1)² + (y − 6)² = 9
- D. (x − 6)² + (y + 1)² = 9
Question 12
A circle has centre (−1, −3) and passes through (−1, 5). Its equation is (x + 1)² + (y + 3)² = k. Find k.
Answer
Question 13
Where is the point (8, 2) relative to the circle (x + 1)² + (y − 1)² = 64?
- A. Inside the circle
- B. On the circle
- C. Outside the circle
Question 14
Which is the equation of the circle with centre (3, −6) and radius 7?
- A. (x − 3)² + (y + 6)² = 7
- B. (x + 6)² + (y − 3)² = 49
- C. (x − 3)² + (y + 6)² = 49
- D. (x + 3)² + (y − 6)² = 7
Question 15
A circle has centre (3, 3) and passes through (1, 0). Its equation is (x − 3)² + (y − 3)² = k. Find k.
Answer
Question 16
Where is the point (−3, 3) relative to the circle (x + 3)² + (y − 4)² = 16?
- A. Inside the circle
- B. On the circle
- C. Outside the circle
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