1, if AO=AP, draw a circle with A as the center and AO as the radius, and the X axis is at point P 1, which is obviously P1(4,0).

2. If OA=OP, draw a circle with O as the center and OA as the radius, and intersect the X axis at points P2 and P3, then OP2=OP3= root number 5, so P2 (root number 5,0 0) P3 (negative root number 5,0).

3. If PA=PO, the middle vertical line of OA intersection G intersects with p4, and the vertical line of X-axis intersection D intersects with A, the triangle OGp4 is similar to the triangle OAD, and it is obtained that Op4=5/4, so P4 (5/4,0).