【摘要】对于二次曲面的分类与化简,一般是首先确定二次曲面的对称面，使对称面为新坐标系的坐标面，然后通过坐标系的平移、旋转，把二次曲面方程分类并化简为标准方程，本文在现有研究成果的基础上，利用配方法、合同变换法、正交变换法给出了二次曲面方程化简的几种途径，从而解决利用坐标系的平移、旋转、不变量对二次曲面方程进行分类、化简时运算复杂或者无法确定图形具体位置等问题，深入探讨二次曲面方程化简与分类的新方法，最后将一般二次曲面方程分类与化简融入实际应用。

【关键词】二次曲面； 分类； 化简；

【Abstract】For the classification and simplification of quadric surface equation, the plane of symmetry of quadric surface, which becomes coordinate plane of the new coordinates, should be defined first. Then simplify and classify the quadric surface equation into standard equation by translation and rotation of the coordinates. This dissertation is based on the existing researches and presents several ways of simplifications of quadric surface through the methods of completing the square, congruent transformation and orthogonal transformation to solve the problems, such as complex calculations or difficulties in confirming the specific positions of graphs, which occur when the quadric surface equation is simplified and classified by the translation, rotation and invariant of coordinates. Moreover, it also has a deep discussion about the new methods for classifications and simplifications of quadric surface equation.

【Key words】Quadric surface; Classification; Simplification;