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本文介绍笔者发现的有关圆锥曲线的一个定理.因为它涉及到三个垂足,所以暂且将它命名为圆锥曲线的三垂足定理.定理在圆锥曲线上任取一点为切点作切线,过该切点作焦点所在的坐标轴的垂线得垂足Ⅰ,过焦点作该切线的垂线得垂足Ⅱ,相应于该焦点的准线与该坐标轴的交点为垂足Ⅲ.则该切点到垂足Ⅱ的距离与该焦点到垂足Ⅱ的距离之比等于垂足Ⅰ到垂足Ⅱ的距离与垂足Ⅲ到垂足Ⅱ的距离之比.不失一般性,设圆锥曲线的焦点在横坐标轴上;
In this paper, we introduce a theorem about the conic found by the author. Because it involves three vertical feet, so for the time being it is named the three-drop theorem of conic. Theorem Theoretically, taking a point as a tangent to a tangent point, Cut point for the focus of the vertical axis of the axis of the foot I have foot I, the focal point of the tangent of the vertical line was enough foot II, corresponding to the focus of the line of intersection with the axis of the foot for the foot III. The cut The ratio of the distance from the point of footing II to the distance of this foot to footing II is equal to the ratio of the distance from footing I to footing II to the distance from footing III to footing II. Without loss of generality, Focus on the abscissa axis;