二次曲线与其任意两条切线所围面积为定常值的问题研究

ON THE PROBLEM THAT THE AREA OF A CURVE OF SECOND DEGREE WITH ITS TWO TANGENTS IS CONSTANT

本文得到了二次曲线的任意两条相交切线与曲线本身围成的面积如果为定常值,则切线交点的轨迹仍为同类型二次曲线.又若给定两条同类的二次曲线,由其中一条上的每一点向另一条引出两条切线,则这两条切线与另一条曲线围成的面积为定常值.

In this paper we obtain two conclusions on quadric curves. First, for any quadric curve, the locus of the intersection point of its two arbitrary tangents is still a quadric curve with the same type, if the area enclosed by the two tangent and the original curve is a constant. Secondly, for any two given quadric curves of the same types, the area enclosed by one curve and the two tangents of the curve,whose common point is an arbitrary point of the other curve, is a constant.