数学必修2：求过三点O(0,0),M1(1,1),M2(4,2)的圆的方程.就是F后面的+2,+20,怎么来的?求过三点O(0,0),M1(1,1),M2(4,2)的圆的方程.按人教A版必修2里面列的是以下的三元一次方程组：F=0D+E+F+2=04D+2E+F+20=0把那3个坐标代入以后,很明显没有可以代入F那里的,我搞不通F后面加的数都哪里来的啊.就是F后面的+2,+20.

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圆的标准方程是 x^2+y^2+Dx+Ey+F=0
则有 0+0+0+0+F=0
1^2+1^2+1XD+1XE+F=0
4^2+2^2+4XD+2XE+F=0

x^2+y^2+Dx+Ex+F=0是圆的一般方程
F=0是把O(0,0)带入的结果
M1(1,1)带入就是1+1+D+E+F=0即D+E+F+2=0
M2(4,2)带入就是16+4+4D+2E+F=0即4D+2E+F+20=0
希望对你有帮助!↖(^ω^)↗

圆的方程为X^2+y^2+Dx+Ey+F=0代入三点。第一个点（0,0），所以得出F=0.而第二地三个点 X，Y代入数字。那个2是代入（1.1）后得：1+1+D+E+F=0 即D+E+F+2=0 同理 那个20 则是代入（4,2）后 16+4+4D+2E+F=O 这样就得到了