两二次曲线公有元素的图解方法

图解两二次曲线的公有元素是平面几何问题,但在二维平面中直接图解该类问题较为困难.根据二次曲线可作为二次曲面截交线的原理,将所给定的两二次曲线通过不同的投影法构造出相应的二次曲面,把二次曲线作为其截交线的投影,图解两二次曲线的公有元素.这样不仅给出了简明直观地求解两二次曲线公有元素的图解方法,同时也为图解平面几何问题提供了一种以空间作为媒介、借助于投影解题的新思路.

Graphic Method of the Intersections and Common Tangents of Two Conics

The common elements of two conics, i.e., the intersections and the common tangents, should be solved in the study of projection theory and some engineering problems. It is rather difficult to find an appropriate graphic method in a two-dimensional plane. This paper presents a concise but effective method for solving the common elements of two conics graphically. As a conic can be regarded as the intersecting transversal of quadrics, the corresponding quadrics may be determined first by different projection methods. The graphic solution of the common elements of the prescribed conics can then be achieved with resort to three-dimensional space transformation and projection methods. The proposed method may be used for reference in other plane geometry problems.