解析几何中的定点问题一直是高考的一个热点问题,笔者最近在研究高考试题时发现2008年江苏卷第18题的动圆过定点问题很有趣,深入研究后发现其命制背景甚为简洁,本文通过该题来谈谈此类动圆过定点问题的几何背景.问题(2008年江苏卷第18题)S在平面直角坐标系xOy中,记二次函数f(x)=x~2+2x+b(x∈R)与两坐标轴有三个交点.经过三个交点的圆 Analysis of fixed-point geometry has been a hot issue in the college entrance examination, the author recently found in the entrance examination papers found that the first 18 questions in Jiangsu in 2008 fixed-point issue is very interesting, in-depth study found that the life background is very simple, In this paper, we will discuss the geometric background of such fixed-point problem through this problem. (In the 18th volume of Jiangsu Volume 2008), in the plane rectangular coordinate system xOy, the quadratic function f (x) = x ~ 2 + 2x + b (x∈R) There are three intersections with two axes