Geometry and TrigonometryVery hardCircumference of a circle from its equation
Geometry and Trigonometry practice question
The equation (x − 2)² + (y + 5)² = 9 represents a circle in the xy-plane. What is the circumference of the circle?
- A. 6πCorrect
- B. 9π
- C. 18π
- D. 3π
Answer: A. 6π
The right side is r² = 9, so r = 3. Circumference = 2πr = 6π.
Why the other answers are wrong
- B. 9π
- 9π is the AREA (πr²).
- C. 18π
- 18π uses r = 9, the value of r², as the radius.
- D. 3π
- 3π uses the radius without the 2 in 2πr.
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