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关于圆锥曲线统一定义与统一方程的教学设计,有些书刊已提出了较好的参考意见。但就教材以及一些数学资料中对此问题的理解却仍有必要探究与商榷,部分教师和很多学生出现的一些模糊看法也有必要澄清。 1.圆锥曲线统一定义的严密性高中数学教材重点中学甲种本《平面解析几何》第174页给出了椭圆、双曲线、抛物线三种圆锥曲线的统一定义,即平面上“与一个定点(焦点(F))的距离和一条定直线(准线(l))的距离的比等于常数e的点的轨迹,当01是双曲线;e=1是抛物线。 (1)对抛物线来说,仅仅强调e=1是不够的,还应强调定点F一定不在定直线L上,
With regard to the unified design of the conical curve and the teaching design of the unified equation, some books and magazines have put forward good reference opinions. However, it is still necessary to explore and discuss the problem in textbooks and some mathematical materials. It is also necessary to clarify some of the vague ideas that some teachers and many students have. 1. Consistency of uniform definition of conical curves High school mathematics textbooks Key secondary schools A type of “flat analytic geometry” on page 174 gives a uniform definition of three kinds of conic curves: ellipse, hyperbola, and parabola. The trajectory of the distance between the focal point (F)) and the distance from a straight line (the quasi-line (l)) equal to the constant e. When 01 is a hyperbola; e=1 It is a parabola (1) For a parabola, it is not enough to emphasize e=1 only, and it should be emphasized that the fixed point F must not be on the fixed line L.