A math problem in Huanggang senior high school entrance examination

As can be seen from the meaning of the question, this problem is to find the range of PA-PB.

| PA-PB | min = 0； (It can be perpendicular to AB, and the focus of L is PA-PB=0)

The key is to find the maximum value of |PA-PB|;

Let pm = x, (0

PA-PB= under radical sign (16+x2)- under radical sign [1+(4-x) 2];

With the ability of junior high school, this formula is really difficult to answer. . . I don't know how to continue,

The first feeling is to ask for guidance directly, but I certainly haven't learned it in junior high school. This is a tragedy.

Let me think about it first. .

As shown in the picture, you have to learn to draw:

In this way, the problem is solved perfectly. . . All you have to do is draw pictures and explain them clearly.