在解析几何的学习中,学生经常会遇到以下两个问题.问题1:到点A(1,1)和到直线x+2y=3距离相等的点的轨迹是什么?问题2:已知动点P(x,y)到点F(1,0)的距离比到y轴的距离大1,则动点P(x,y)的轨迹是什么.本文将对以上两个问题作简要剖析,并适度拓展.一、问题的典型错误与解决对于问题1,在学习了抛物线的定义以后,很多同学会觉得该问题所涉及的轨迹“应该”是抛物线.可事实是不是 Students often encounter the following two problems in analytic geometry Question Q1: What is the trajectory of a point that is equidistant to point A (1,1) and to line x + 2y = 3 Question 2: Known What is the trajectory of the moving point P (x, y) when the distance from the moving point P (x, y) to the point F (1,0) is larger than the distance from the y axis by 1? First, the problem of the typical mistakes and solutions For the problem 1, after learning the definition of the parabola, many students will feel the problem involved in the track “should ” is a parabola.