Geometry and TrigonometryHardEquation of a circle from its centre and a point
Geometry and Trigonometry practice question
In the xy-plane, a circle has centre (2, 3) and passes through the point (5, 7). Which equation represents the circle?
- A. (x − 2)² + (y − 3)² = 25Correct
- B. (x − 2)² + (y − 3)² = 5
- C. (x + 2)² + (y + 3)² = 25
- D. (x − 5)² + (y − 7)² = 25
Answer: A. (x − 2)² + (y − 3)² = 25
Radius² = (5 − 2)² + (7 − 3)² = 9 + 16 = 25.
Why the other answers are wrong
- B. (x − 2)² + (y − 3)² = 5
- 5 is the radius; the equation uses r² = 25.
- C. (x + 2)² + (y + 3)² = 25
- (x + 2)² + (y + 3)² has centre (−2, −3).
- D. (x − 5)² + (y − 7)² = 25
- (5, 7) is a point on the circle, not its centre.
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