二次曲线渐近线与二次曲面渐近面的探究

Exploration of the Asymptote of Conic and the Asymptotic Surface of Quadric

文章对二次曲线的渐近线、二次曲面的渐近面的求法以及共焦二次曲面的基本定理进行了一些探究。根据二次曲线或二次曲面的不同变换形式,探索出多种求解方法;探讨共焦二次曲面的基本定理,并给出详细的证明。

In this paper,we study the asymptote of quadratic curve and the tangent cone of a quadric.A variety of solutions are explored according to the different transformation forms of the quadratic curve and quadric surface.The fundamental theorem of confocal quadric surfaces is discussed,and the detailed proof is given.On the one hand,we can systematically use the knowledge of conic and quadric surface;on the other hand,readers can further understand the essential features which is about the asymptote of quadratic curve and the asymptotic surface of quadric.