Geometry and TrigonometryMediumEquation of a circle from centre and radius
Geometry and Trigonometry practice question
In the xy-plane, a circle has centre (3, −4) and radius 10. Which equation represents the circle?
- A. (x − 3)² + (y + 4)² = 100Correct
- B. (x + 3)² + (y − 4)² = 100
- C. (x − 3)² + (y + 4)² = 10
- D. (x − 3)² + (y − 4)² = 100
Answer: A. (x − 3)² + (y + 4)² = 100
(x − h)² + (y − k)² = r² with h = 3, k = −4, r = 10.
Why the other answers are wrong
- B. (x + 3)² + (y − 4)² = 100
- The signs of the centre are reversed.
- C. (x − 3)² + (y + 4)² = 10
- The right side must be r², 100.
- D. (x − 3)² + (y − 4)² = 100
- The y-term should be y + 4 for k = −4.
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