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求满足条件的动点的轨迹方程,是解析几何的常见问题,大部分同学很容易忽视求出的方程要满足完备性和纯粹性,在实际解题中也不太会讨论,下面给出了求出点的轨迹方程后去“杂”堵“漏”的几种做法。一、利用三角形的顶点不共线去“杂”例1 已知点A(-a,0),B(a,0),a＞0,若△MAB是以点M为直角顶点的直角三角形,求顶点M的轨迹方程。
Finding the trajectory equation of the moving point that satisfies the condition is a common problem of analytical geometry. It is easy for most students to ignore the equations to be satisfied to satisfy the completeness and purity, and it is not likely to be discussed in practical problems. The following is given After calculating the trajectory equation of the point, several approaches to “miscellaneous” blocking “leakage” are proposed. First, use the vertices of the triangle not collinear to “miscellaneous” Example 1 Known points A (-a, 0), B (a, 0), a> 0, if △ MAB is a right-angled triangle with point M as a right-angled vertex , find the trajectory equation of the vertex M.