已知平面上不共线的三点A(x_1,y_1),B(x_2,y_2),C(x_3,y_3),确定经过这三点的(平面直角坐标系下)圆的方程,常规的求法有如下两种:一种是根据圆的几何性质,联立△ABC其中两条边的中垂线(或直接由两点间距离公式建立方程)求出圆心坐标,进而算出半径,列出圆的标准方程;另一种则是用代数方法,设 We know the three points A (x_1, y_1), B (x_2, y_2) and C (x_3, y_3) that are not collinear in the plane and determine the equation of the circle passing through these three points There are two kinds of seeking method: one is to find out the coordinates of the center of the circle according to the geometric property of the circle, the perpendicular bisector of the two sides of △ ABC (or directly from the distance formula between two points), and then calculate the radius, The standard equation of the circle; the other is the algebraic method, set