Geometry and TrigonometryHardEquation of a circle tangent to both axes
Geometry and Trigonometry practice question
In the xy-plane, a circle with radius 3 lies in the first quadrant and is tangent to both the x-axis and the y-axis. Which equation represents the circle?
- A. (x − 3)² + (y − 3)² = 9Correct
- B. x² + y² = 9
- C. (x + 3)² + (y + 3)² = 9
- D. (x − 3)² + (y − 3)² = 3
Answer: A. (x − 3)² + (y − 3)² = 9
Tangent to both axes with radius 3 puts the centre at (3, 3), and r² = 9.
Why the other answers are wrong
- B. x² + y² = 9
- This circle is centred at the origin and crosses both axes.
- C. (x + 3)² + (y + 3)² = 9
- This centre, (−3, −3), is in the third quadrant.
- D. (x − 3)² + (y − 3)² = 3
- The right side must be r² = 9, not 3.
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