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一族平面直线的“包络”是指一条与这族直线中任意一条都相切的曲线。圆锥曲线可以以多种方式看作直线族的包络。本文对原有的包络方式进行推广,使用解析几何的方法证明了圆锥曲线可以由定点和定圆(或定直线)连线的垂线的包络生成。然后,用平面几何的方法推广到了用和定点和定圆(或定直线)连线成定角的直线族包络生成圆锥曲线。最后,本文证明了用和顶点和定椭圆连线的斜率的乘积为定值的直线族的包络也可以生成有心圆锥曲线。
The “envelopes” of a family of planar lines mean a curve that is tangent to any one of the family’s lines. Conic curves can be viewed in many ways as an envelope of a straight line family. In this paper, we extend the original envelope method and prove that the conic curve can be generated by the envelope of the vertical line connecting fixed point and fixed circle (or fixed line). Then, the method of plane geometry is extended to generate the conic curve with the enveloping of the family of lines which is fixed with the fixed point and fixed circle (or fixed line). Finally, we prove that the envelope of a family of straight lines, which is a product of the slopes of the vertex and the fixed ellipse, can also generate conic curves.