《数学通报》2012年11月号上的问题解答栏第2087题为:椭圆的焦点在椭圆切线上的射影的轨迹是以椭圆的中心为圆心,且过长轴顶点的圆.该题提供的方法从方程解交点的角度求出了射影的轨迹方程,但相对比较烦琐.本文将从圆锥曲线切线的性质出发给出一种简便证法,并对结论和研究方法予以推广和反思. Question No. 2087 on the November issue of Mathematics Bulletin No. 2087 is: Focus of an ellipse The trajectory of an ellipse on an elliptical tangent is a circle centered on the center of the ellipse and over the apex of the long axis. Method The trajectory equation of projective trajectory is obtained from the perspective of solution intersection point, but it is relatively cumbersome.This paper will give a simple proof from the nature of the tangent of conic curve, and popularize and reconsider the conclusion and research methods.