二次曲线方程的五点确定法

The Five-point Deterministic Method of Quadratic Curve Equations

由命题和定义,通过实例,首先用待定系数法给出了常态二次曲线方程的确定法;然后按二次曲线的射影定义给出了常态二次曲线方程的另一种确定法;再利用二次曲线束的概念求得了变态二次曲线和常态二次曲线的方程;最后求曲线束中的降秩二次曲线,令其系数行列式为零,则给出了二次曲线方程组的解法.

Based on definitions and propositions and examples, it is first proposed the method ot uncleter- mined coefficients for normal quadratic curve equations. According to the projective definition of quadratic curves, another deterministic method is given for the same equation. The definition of quadratic curve bunches is used to obtain the equations of metamorphosis and normal quadratic curves. Finally, a solution is given to the system of quadratic curve by letting the corresponding determinant be zero for rank-reduced quadratic curves in the curve bunches.