论文部分内容阅读
题目在平面直角坐标系xOy中,设二次函数f(x)=x2+2x+b(x∈R)的图象与两坐标轴有三个交点,经过这三个交点的圆记为C.(Ⅰ)求实数b的取值范围;(Ⅱ)求圆C的方程;(Ⅲ)问圆C是否经过定点(其坐标与b无关)?请证明你的结论.这是2008年高考江苏卷理科第18题,是一道以对称轴固定的动态抛物线与两坐标轴有三个交点以及经过这三个交点的动圆为载体的解析几何题,重点考查动圆的方程和证明动圆过定点,同时考查运算能力和推理论证能力.本文给出第(Ⅱ)
Subjects In the Cartesian coordinate system xOy, let the image of the quadratic function f (x) = x2 + 2x + b (x∈R) have three points of intersection with the two axes, and the circle passing through these three points is denoted by C. (Ⅰ) Obtain the range of the real number b; (Ⅱ) Find the equation of the circle C; (Ⅲ) Ask whether the circle C has been fixed point (its coordinates have nothing to do with b); Please prove your conclusion. Science Question 18 is an analytical geometry problem with three axes of dynamic parabola and two axes fixed by a symmetry axis and a moving circle passing through the three intersections. The focus is on examining the moving equation and proving that the moving circle passes through a fixed point, At the same time to examine the computing power and reasoning ability of argumentation.This paper gives the (Ⅱ)