This problem is simple and intuitive, but it is complicated and troublesome to use other methods, which can provide a reverse idea for the landlord's reference.

According to PA PB =- 1, the angle between vector PA and vector PB is π, and then it is known that the trajectory of point p must be within the ellipse given by the problem condition, and the result of multiplying the length of line segment PA by the length of line segment PB is 1.

Note also that when both A and B are greater than 0, when a+b= constant C, and if and only if a=b=C/2, ab takes the maximum value.

Therefore, when the straight line L moves to L: x = √ 2 and the point P falls on the X axis, when L moves between X = √ 2, there are two moving points corresponding to the point P above and below the X axis respectively. Therefore, after determining the coordinates of point P on the X axis and then on the Y axis, we can guess that the trajectory of point P is an ellipse, hoping to help the landlord.