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! ]