Geometry and TrigonometryHardCircle through the origin with centre on the y-axis
Geometry and Trigonometry practice question
A circle in the xy-plane has its centre at (0, 4) and passes through the origin. Which equation represents the circle?
- A. x² + (y − 4)² = 16Correct
- B. x² + (y + 4)² = 16
- C. x² + (y − 4)² = 4
- D. (x − 4)² + y² = 16
Answer: A. x² + (y − 4)² = 16
The radius is the distance from (0, 4) to (0, 0), which is 4. So (x − 0)² + (y − 4)² = 4² = 16.
Why the other answers are wrong
- B. x² + (y + 4)² = 16
- (y + 4)² puts the centre at (0, −4).
- C. x² + (y − 4)² = 4
- The right side is r² = 16, not the radius 4.
- D. (x − 4)² + y² = 16
- (x − 4)² + y² has its centre at (4, 0), on the x-axis.
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