圆锥曲线的公切圆作图法

A NEW METHOD TO DRAW CONICAL CURVES BY THE COMMON TANGENT CIRCLE

本文详细分析、探讨了公切圆圆心轨迹曲线。得出并证明了:以同一种方式公切于两定圆,所有公切圆上的对应切点连线,必交于两定圆的相似中心。在此基础上,提出了简便、实用的圆锥曲线公切圆作图法。它与文献[2]所提出的圆锥曲线垂足点作图法,有着本质上的内在联系,但更简便、实用。与目前常用的两同心圆作椭圆[4]相比,省去了推平行线的麻烦。

The curve of locus about the centers of common tangent circles is analysed and discussed in detait in this paper. It reaches the conclusion that the lines connecting two correseponding tangent points on all the circles, which are tangential commonly to two definite circles in the same way , must intersect at conformal center of the two definite circles. On this basis, a practical simple way to construct by the conical curves the common tangent circle is presented. It has internal relation to the method of drawing perpendicular base of conical curves in reference (2). But it is simpler and more practical. Compared with the usual method to draw ellipse by two concentric circles, it relieves the work to plot parallel lines.