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1.引言.本文給出一个决定拋物綫开口方向的一个簡单办法:即証明当二次曲綫 Ax~2+2Bxy+Cy~2+2Dx+2Ey+F=0 (1)是拋物綫时(在直角坐标或仿射坐标中),它开口的方向是向量(BE—CD,DB—AE)所指的方向。另外,关于一般二次曲綫(1)的两个問題,即根据(1)底系数来判断它底軌迹底形状和确定这軌迹在所給坐标系中的位置的有关問題,在一些书上是分开来討論的。(見[1]和[2])这是由于后一問題需要引入較多的概念和牽涉到較深的理論。另一些书上,为了精簡教材(見[3]和[4]),用移軸和轉軸的办法尽可能地把这两个問題統一起来处理,但有些重要結果和簡便方法尚未能包括进去。对此,本文提出几点补充注意,說明怎样可
1. Introduction. This article presents a simple way to determine the direction of the opening of a parabola: prove that when the quadratic curve Ax~2+2Bxy+Cy~2+2Dx+2Ey+F=0 (1) is a parabola ( In Cartesian or affine coordinates, the direction in which it opens is the direction of the vector (BE-CD, DB-AE). In addition, regarding the two problems of the general quadratic curve (1), that is, according to (1) the bottom coefficient to determine its bottom trajectory bottom shape and the problem of determining the position of the trajectory in a given coordinate system, in some books is Discuss it separately. (See [1] and [2]) This is because the latter problem requires the introduction of more concepts and involves deeper theories. In other books, in order to streamline the teaching materials (see [3] and [4]), the two problems are unified as much as possible by shifting the axis and rotating the axis, but some important results and simple methods have not yet been included. . In this regard, this article proposes several additional notes that explain how