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我们知道,圆的传统定义是:平面内到一个定点的距离等于定长的点的轨迹叫做圆。这里我向读者介绍圆的另一定义。定义平面内与两个定点F_1、F_2的距离的平方和等于常数(大于1/2|F_1F_2|~2)的点的轨迹叫做圆。圆的这一定义完全可以和椭圆定义相媲美,其科学性是不难验证的,证明如下: 取过定点F_1、F_2的直线为x轴,线段F_1F_2的垂直平分线为y轴,建立直角坐标系。设动点为P(x,y),|F_1F_2|=2c(c>0),P与F_1和F_2
We know that the traditional definition of a circle is that the trajectory of a point within a plane to a fixed point equal to a fixed-length point is called a circle. Here I introduce the reader to another definition of a circle. The trajectory defining the sum of the squares of the distances between the plane and the two fixed points F_1 and F_2 equal to a constant (greater than 1/2|F_1F_2|~2) is called a circle. This definition of circle can be completely comparable to the definition of ellipse. Its scientificity is not difficult to verify. It is proved as follows: The straight line that takes the fixed points F_1 and F_2 is the x-axis, and the vertical bisector of the line segment F_1F_2 is the y-axis, and the rectangular coordinate is established. system. The setpoint is P(x,y), |F_1F_2|=2c(c>0), P and F_1 and F_2