本文探讨了圆锥曲线的三种伴随曲线 ,从而揭示了圆锥曲线的几个有趣的性质 .引理 1 [1 ] 　关于ｘ、ｙ的二元一次方程(1 -ｅ2 )ｘ2 +ｙ2 - 2ｐｘ+ｐ2 =0(ｐ0 ,ｅ 0 ) ①当ｅ=1时表示抛物线 ,当 0 ｅ1时和ｅ 1时分别表示以 ｐ1 -ｅ2 ,0为中心的椭圆和双曲线 .引理 2　过圆 This paper explores three concomitant curves of conic curves, revealing several interesting properties of conic curves. Lemma 1 [1] Binary equations for x, y (1 - e2) x2 + y2 - 2px + p2 =0(p0,e0) 1 When e=1, it means a parabola, when 0e1 and e1 respectively represent ellipses and hyperbolas centered on p1 -e2,0. Lemma 2 round