解:(1)

,

.························································· 1分
當

時,

,

.
所以直線
AB與
CD交點的坐標為

.···················································· 2分
(2)

當0<

<

時,△
MPH與矩形
AOCD重合部分的面積即△
MPH的面積.
過點
M作

,垂足為
N.
由△
AMN∽△
ABO,得

.
∴

.∴

.········································································ 4分
∴△
MPH的面積為

.
當

時,

.············································································· 5分
當

<

≤3時,設(shè)
MH與
CD相交于點
E,△
MPH與矩形
AOCD重合部分的面積即
△
PEH的面積.
過點
M作

于
G,

交
HP的延長線于點
F.



.

.
由△
HPE∽△
HFM,得

.
∴

.∴

.································································ 8分
∴△
PEH的面積為

.
當

時,

.
綜上所述,若△
MPH與矩形
AOCD重合部分的面積為1,

為1或

.·················· 9分
(3)

有最小值.
連接
PB,
CH,則四邊形
PHCB是平行四邊形.
∴

. ∴

.
當點
C,
H,
Q在同一直線上時,

的值最。ぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁ 11分
∵點
C,
Q的坐標分別為

,

, ∴直線
CQ的解析式為

,
∴點
H的坐標為

. 因此點
P的坐標為

.······························ 12分