在平面几何中,设O是圆中定弦AB的中点,过O作两条任意弦CD和GH,若CH和GD分别交AB于P和Q,则OP=OQ(如图)。这就是著名的“蝴蝶定理”。笔者认为上述结论,可以推广到圆锥曲线中,为此,先证明以下引理:引理:以圆锥曲线的一条对称轴为y轴,轴上的点O为原点建立直角坐标系,若过点O的直线 In plane geometry, let O be the midpoint of a constant AB in the circle, and let O be two arbitrary strings CD and GH. If CH and GD intersect AB in P and Q, then OP = OQ (see figure). This is the famous “butterfly theorem.” The author believes that the above conclusion can be extended to the conic. To prove this, we first prove the following lemma: Lemma: If one axis of symmetry of the conic is the y-axis and the point O on the axis is the origin, a rectangular coordinate system will be established. O of the straight line