Geometry and TrigonometryVery hardEquation of a circle tangent to the x-axis
Geometry and Trigonometry practice question
In the xy-plane, a circle has centre (2, −3) and is tangent to the x-axis. Which equation represents the circle?
- A. (x − 2)² + (y + 3)² = 9Correct
- B. (x − 2)² + (y + 3)² = 4
- C. (x + 2)² + (y − 3)² = 9
- D. (x − 2)² + (y + 3)² = 3
Answer: A. (x − 2)² + (y + 3)² = 9
Tangent to the x-axis means the circle just touches it, so the radius equals the centre's distance from the x-axis: |−3| = 3. Then (x − 2)² + (y + 3)² = 3² = 9.
Why the other answers are wrong
- B. (x − 2)² + (y + 3)² = 4
- 4 would be r² = 2², using the centre's x-coordinate as the radius.
- C. (x + 2)² + (y − 3)² = 9
- (x + 2)² + (y − 3)² has centre (−2, 3).
- D. (x − 2)² + (y + 3)² = 3
- The right side must be r² = 9, not r = 3.
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