It is known that the images of linear function y=2x-k and inverse proportional function y=k+2/x intersect at points a and b,

The abscissa of an intersection a is 3.

(1) Find the relationship between the two functions respectively.

(2) Find the coordinates of point A and point B and the area of triangle AOB.

(3) If there is a point P on the straight line AB, make the triangle APO similar to the triangle AOB, and find the coordinates of the point P.