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所谓转移法,就是在给出的问题中若出现二个动点,其中一个动点M(x_1,y_1)在已知曲线C:F(x,y)=0上运动,所要求的轨迹的动点P(x,y)与点M(x_1,y_1)有一定的联系,这种联系可以用某一关系式表示,把关系式代入F(x,y)=0中即可得点P的轨迹方程,此方法谓之为“转移”,即根据P点与M点的联系,利用点M在已知曲线上运动,而将P点转移给M点,从而求得P点的轨迹方程。如:“已知P为圆x~2+y~2=4上一个动点,又点Q的坐标为(4,0),试求线段PQ的中点轨迹方程”。
The so-called transfer method is that if there are two moving points in the given problem, one of the moving points M(x_1, y_1) moves on the known curve C:F(x,y)=0, and the required trajectory The moving point P(x,y) has a certain relation with the point M(x_1,y_1). This connection can be represented by a certain relational expression. Substituting the relational expression into F(x,y)=0 can obtain the point P. Trajectory equation, this method is called “transfer”, that is, according to the connection between P point and M point, point M is used to move on the known curve, and P point is transferred to M point, so as to obtain the trajectory equation of P point. Such as: “P is known to be a point on the circle x ~ 2 + y ~ 2 = 4 points, and point Q coordinates (4,0), try to find the midpoint trajectory equation of the line segment PQ”.