现行高二《解析几何》教材第二章有这样一道题:已知一曲线是与两个定点O(0,0),A(3,0)距离的比等于1/2的点的轨迹,求这个曲线的方程。通过简单的分析解答,得知曲线方程是(x+1)~2+y~2=4,而动点的轨迹是以C(-1,0)为圆心、r=2为半径的圆。由C(一1,0)易知,C在x轴上广(见图1)即C在直线OA上。 The second chapter of the current high school “Analytic Geometry” textbook has this question: Knowing that a curve is a trajectory with a point where the ratio of two fixed points O(0,0) and A(3,0) is equal to 1/2, find The equation of this curve. Through a simple analytical solution, we know that the curve equation is (x+1)~2+y~2=4, and the trajectory of the moving point is a circle with C(-1,0) as the center and r=2 as the radius. It is easy to know from C(-1,0) that C is wide on the x-axis (see Figure 1), that is, C is on the straight line OA.