解析法就是通过点的坐标,线的方程的计算与讨论,从而获得解决问题的方法。它的特点是以“坐标”为桥梁,使几何学的“形”与代数学的“数”互相沟通,互为其用。在解题中能起到简捷直观的作用,并能激发学生浓厚的学习兴趣及求知欲。现就它在代数,三角中的应用列举数例。例1 m为何值时,直线l:y=-x+m曲线C:y=1/2(20-x~2)~(1/2)+1有一个公共点?有两个公共点?无公共点? 解如图(1),C为半椭圆,设直线l_1:y=-x+m_1与C相切,直线l_2:y=-x+m_2与l_3:y=-x+m_3分别交C于A、B点,C的 The analytical method is to obtain the solution to the problem by calculating and discussing the coordinates of the point and the equation of the line. Its characteristic is that it uses “coordinates” as a bridge to make the “form” of geometry and the “number” of algebra communicate with each other. Can play a simple and intuitive role in the problem solving, and can stimulate students a strong interest in learning and curiosity. Here are a few examples of its use in algebra and trigonometry. Example 1 When m is the value, the line l:y=-x+m Curve C:y=1/2(20-x~2)~(1/2)+1 Has a common point? Has two common points? No common point? Solution: (1), C is a semi-ellipse, set the line l_1:y=-x+m_1 to be tangent to C, and the lines l_2:y=-x+m_2 and l_3:y=-x+m_3 respectively. Submit C to A, B, C’s