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《数学通报》数学问题2 087实质上证明了:结论1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.我们知道,“焦点”是一个特殊的点,轨迹是一个“圆”.若是椭圆轴上任意一定点,其在椭圆切线上的射影的轨迹一定不是一个圆,那它的轨迹又是什么呢?笔者通过探索得出其轨迹方程,并借助数学作图软件直观的作出了这些方程所表示的曲线,所得图形美的奇异、对称,宛似数学百花园中的一簇美丽小花.
Mathematical Problem Mathematics 2 087 is essentially proof of the following: Conclusion 1 The trajectory of the ellipse’s focal point on an elliptical tangent is a circle centered on the center of the ellipse and over the apex of the long axis. We know that the “focus” Is a special point, the trajectory is a “circle ” If any point on the elliptical axis, the trajectory of the projection on the elliptical tangent must not be a circle, then what is the trajectory of it? I explore Out of its trajectory equations and intuitively make use of mathematical mapping software to make the curves represented by these equations. The resulting figures are beautiful, symmetrical, and graceful like a cluster of beautiful flowers in a hundred flower gardens.