我们通常把椭圆或双曲线上一点与其两个顶点围成的三角形称为它的顶点三角形,而将抛物线上两点与其顶点围成的三角形称为抛物线的顶点三角形.在研究圆锥曲线时,笔者发现由其顶点三角形生成的圆具有以下有趣性质.定理1设A、B是椭圆C:x2/a2+y2/b2=1(a>b>0)的左、右顶点,P是椭圆上异于A、B的任意一点,不经过点P的定直线l:x=t与x轴交于点D,与直线PA、PB分别交于M、N两点. We usually call the triangle formed by the point on the ellipse or hyperbola and the two vertices of the triangle as its vertex triangle and the triangle formed by the two points on the parabola and its vertex as the vertex triangle of the parabola. Find the circle generated by its vertex triangle has the following interesting properties: Theorem 1 Let A and B be the left and right vertices of the ellipse C: x2 / a2 + y2 / b2 = 1 (a> b> 0) At any point of A, B, without going through the point P of the fixed line l: x = t intersect with the x-axis point D, and the lines PA, PB, respectively, at M, N points.