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曲线y=x² -6x+1与y轴的交点: D(0, 1) y = x² -6x+1 = 0, x = 3±2√2, 与x轴的交点: A(3-2√2, 0), B(3+2√2, 0) 曲线y=x² -6x+1为抛物线,对称轴为x = 3 显然圆心C在对称轴上,设C(3, b) CA = CD = r CA² = CD² (3 - 3 + 2√2)² + (b - 0)² = (3- 0)² + (b - 1)² 8 + b² = 9 + b² - 2b + 1 b = 1 C(3, 1) C, D的纵坐标相同,距离为横坐标之差, r = 3-0 = 3 圆C的方程: (x - 3)² + (y - 1)² = 9
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