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求曲线方程是解析几何的基本问题,常用的方法有直接法、定义法、参数法(包括转移法、交轨法,其本质也是参数法).自从新课程增加了平面向量的内容后,向量常被作为一种工具用于证明平行和垂直,也常用于求角和距离.但是,还有值得我们关注的是:用向量求曲线的方程,尤其是当曲线的约束条件涉及到“垂直”或“平行”时,用向量来求解,相对于上述方法,往往会更为明快和简捷.归结起来,有下列情形:
Finding the curve equation is the basic problem of analytical geometry. The commonly used methods include direct method, definition method, and parameter method (including transfer method and cross-track method, whose essence is also the parameter method). Since the new course added the content of the plane vector, the vector It is often used as a tool to prove parallelism and perpendicularity. It is also commonly used to evaluate angles and distances. However, there is something worthy of our attention: Equations for solving curves with vectors, especially when the constraints of the curve involve vertical When “” or “parallel” is used, the vector is used to solve. Relative to the above method, it is often more clear and simple. In summary, there are the following situations: