二次型化简二次曲线方法的探究

Research on the Simplification of Second-order Curves to Normal Curves

通过结合解析几何与代数理论知识,利用化二次型为标准形的通常方法,给出了化简二次曲线的两种思路:合同变换和正交变换.前者是在不着重研究曲线几何性质时常用的一种方法,它的标准型不唯一,而后者相反.文中讨论了它们在实际例题中的应用.

We present two approaches to simplify second-order curves： the congruent and orthogonal transfonn, which are based on analytic geometry, algebra theory, and the ordinary approaches of the simplification of second-order curves to normal ones. The congruent transform is an approach that does not emphasize the geometric propeties of curves, and whose normal form is not unique. However, the orthogonal transform is an opposite approach. We also discuss their applications to practical instances.