大家知道,椭圆和双曲线已经有两个定义,第一个定义是用平面内的动点与两个定点的距离的和或差为常数来描述的;第二个定义是用平面内的动点到一个定点的距离与它到一条定直线的距离的比为常数来描述的. 下面用平面内的动点与两个定点的连线的斜率的乘积为定值给出椭圆和双曲线的又一个定义(如图). As you know, there are two definitions of ellipses and hyperbolas. The first definition is to describe the sum or difference of the distances between the moving points in the plane and the two fixed points as a constant; the second definition is to use the motion in the plane. The ratio of the distance from a fixed point to its distance from a fixed line is described as a constant. The product of the slope of the line connecting the fixed point and the two fixed points in the plane is given as an ellipse and a hyperbolic curve. Another definition (pictured).