Solution: (1) connect PC, PA and PB, so that the PH⊥x axis passes through point P, and the vertical foot is H. .........................................................................................................................

⊙⊙P is tangent to the axis at point C (0 0, 1),

∴PC⊥ axis

∵P point is on the image of inverse proportional function,

The coordinate of point p is (k, 1) ..................................................................................................................................................

∴PA=PC=k.

At Rt△APH, AH==,

∴OA=OH—AH=k-.

∴ A (k-，0) .............................................................................................................................................................

From ∫ to ⊙ to ⊙W to w

∴OB=OA+2AH= k-+2=k+，

∴B(k+, 0 points) 4 points.

Therefore, the analytical formula of the straight line whose parabola axis of symmetry passes through point A and point B is PH is X = K. 。

The analytical formula of this parabola can be set to y = a+h. 5 point.

The parabola passes through c (0, 1) and B(k+ 0) again, and we get:

The solution is a= 1 and h = 1- ..............................................................................................................................................

The analytical formula of parabola is y =+ 1-...8 minutes.

(2) According to (1), the D coordinate of the parabola vertex is (k, 1-).

∴DH=- 1.

If the quadrilateral ADBP is a diamond, then there must be pH = DH. ............................................................................................................................................................

∵PH= 1,∴- 1= 1.

∫k > 1, ∴ k = ...................................11min.

∴ When k is taken, PD and AB are divided vertically, and the quadrilateral ADBP is a diamond. ................................................................................................................................................

[Note: There are different solutions to the above questions. Please refer to the grading for the correct answer! ]