Question 3
Coordinate GeometryA circle has its centre on the x-axis and passes through (1, 2) and (3, 2), find its equation.
- A.x2 + y2 − 4x − 1 = 0
- B.x2 + y2 + 4x + 1 = 0
- C.x2 + y2 − 1 = 0
- D.x2 + y2 − 4x + 1 = 0
Show the answer and explanation
Answer: A (x2 + y2 − 4x − 1 = 0)
Explanation
The centre (a, 0) is equally far from both points, so a = 2. r² = (1 − 2)² + 2² = 5. (x − 2)² + y² = 5 expands to x² + y² − 4x − 1 = 0.