旋转抛物面的新定义及其性质

New Definition and Properties of Rotating Paraboloid

从点的轨迹的角度,将R3中的旋转抛物面定义为:R3中到一定点与到一定平面(点不在平面上)距离相等的点的轨迹.同时引入旋转抛物面的焦点、准平面、准线等概念,并在此基础上证明关于旋转抛物面的焦点弦、准平面、顶点、对称轴、切平面之间的若干重要性质.

Considering it as the locus of points,we define rotating paraboloid inR3： It is a locus of the variable points,from which the distance to a fixed point equates that to a definite plane away from the variable point（the fixed point does not belong to the definite plane）.By introducing the definition of the focus,directrix plane,directrix of the rotating paraboloid,we prove some important properties among the focal chord,the directrix plane,the vertex,the axis of symmetry and the tangent plane of the rotating paraboloid.