1问题提出平面解析几何中利用平面内到两定点的距离构造椭圆、双曲线、圆,这三种曲线的构造分别用动点到两定点的距离的和、差、商为定值的形式给出.在四种算术运算中,唯独没有积,那么平面内与两定点距离之积是常数的点的轨迹是怎样的呢?可以利用GeoGebra的绘制隐函数图象的功能进行探索! 1 PROBLEM PROBLEMS In the plane analysis geometry, the elliptic, hyperbolic, and circular curves are constructed by using the distance from the plane to the two fixed points. The constructions of the three curves are respectively given as the sum of the distances from the moving point to the two fixed points, Out of the four arithmetic operations, there is no product, so what is the trace of the point where the product of the distance between two points in the plane is constant? You can use GeoGebra’s function of drawing implicit functions to explore!