现行高中《平面解析几何》课本中有这样一个命题[1]:“点M与点F(4,0)的距离比它到直线x+5=0的距离小1,求点M的轨迹方程,”对基础较好的学生来说会联想到用抛物线的定义去解非常简单,它等价于命题“点M与点F(4,0)的距离等于它列直线x=-4的距离,求点M的轨迹方程。”很明显答案为y~2=16x,解法很巧妙! There is a proposition [1] in the current high school “Flat Analytical Geometry” textbook: “The distance between the point M and the point F (4,0) is one less than the distance from the point x+5=0, and the trajectory equation of the point M is obtained. ,” For students with a better foundation, it would be very easy to think about solving with a parabolic definition. It is equivalent to the proposition "The distance between point M and point F (4,0) is equal to the distance between its column x = -4. Find the trajectory equation for point M.” The obvious answer is y~2=16x, and the solution is clever!