Geometry and TrigonometryVery hardEquation of a circle from centre and radius
Geometry and Trigonometry practice question
Which equation represents the circle in the xy-plane with centre (−1, 4) and radius 3?
- A. (x + 1)² + (y − 4)² = 9Correct
- B. (x − 1)² + (y + 4)² = 9
- C. (x + 1)² + (y − 4)² = 3
- D. (x + 1)² + (y − 4)² = 6
Answer: A. (x + 1)² + (y − 4)² = 9
The standard form is (x − h)² + (y − k)² = r². With h = −1, k = 4 and r = 3: (x − (−1))² + (y − 4)² = 3², which is (x + 1)² + (y − 4)² = 9.
Why the other answers are wrong
- B. (x − 1)² + (y + 4)² = 9
- Both signs are flipped. Subtracting h = −1 gives x + 1, and subtracting k = 4 gives y − 4.
- C. (x + 1)² + (y − 4)² = 3
- The right side must be r² = 9, not r = 3.
- D. (x + 1)² + (y − 4)² = 6
- 6 is 2r, not r². The radius is squared: 3² = 9.
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