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关于一般二次曲线方程的讨论,是解析几何中理论性较强的内容之一,它是中学数学二次曲线标准方程的推广,又是进一步学习一般二次曲面方程的讨论的基础和准备。一般二次曲线方程的讨论,包括用坐标变换的方法化简一般二元二次方程为标准形式,从而对一般二次曲线进行分类,并作出图形。还包括用不变量来判别一般二次曲线的类型,以及用不变量直接写出化简后的方程,从而确定曲线的形状和大小。在这两种方法中,坐标变换的方法是基本的,不变量
The discussion about the general quadratic curve equation is one of the theoretically strong contents in analytic geometry. It is the generalization of the secondary equation of the secondary curve of middle school mathematics, and it is also the foundation and preparation for the further study of the general quadric equation. The discussion of the general quadratic curve equations, including the use of coordinate transformation methods to simplify the general quadratic quadratic equation as the standard form, thus classifying the general quadratic curve and making a graph. It also includes the use of invariants to discriminate the type of general quadratic curves, and the use of invariants to directly write simplified equations to determine the shape and size of the curve. In both methods, the method of coordinate transformation is basic, invariant