Question Detail
Question
Find the equation of a circle passing through the point (4,1) and (1,5) and having its center on the x-axis.
Correct Answer
Option B is the correct answer.
Detailed Explanation
Center on x-axis means (h,0). Distance to (4,1) and (1,5) are equal: (h-4)² + 1² = (h-1)² + 25 → h² - 8h + 16 + 1 = h² - 2h + 1 + 25 → -8h + 17 = -2h + 26 → -6h = 9 → h = -1.5. Center (-1.5,0). Radius² = (-1.5-4)² + 1² = (-5.5)² + 1 = 30.25 + 1 = 31.25. Equation: (x+1.5)² + y² = 31.25 → x² + 3x + 2.25 + y² = 31.25 → x² + y² + 3x - 29 = 0. That matches option C.
Hint
Set center as (h,0) and use equal distances.