试题分析:(1)过点A作AE⊥OB于点E,在Rt△OAE中求AE的长,然后再在Rt△BAE中求出AB的长,进而求出面积的表达式,结合定义域,根据一次函数的性质确定最大最小值;
(2)相切时有两种情况,在第一象限或者第四象限,连接OA,并过点A作AE⊥OB于点E,在Rt△OAE中求出OE,然后就能求出A点坐标,AB所在直线对应的函数关系式很容易就能求出.
试题解析:(1)如图1,连接OA,过点A作AE⊥OB于点E,
在Rt△OAE中,
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032006787747.png)
,
在Rt△BAE中,
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408230320068021580.png)
,
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408230320068491620.png)
,其中-1≤x≤1.
∴当x=-1时,S的最大值为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032006724498.png)
,当x=1时,S的最小值为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032006740493.png)
.
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408230320068808948.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408230320068968647.png)
(2)①当点A位于第一象限时(如图1),连接OA,并过点A作AE⊥OB于点E,
∵直线AB与⊙O相切,∴∠OAB=90°.
又∵∠CAB=90°,∴∠CAB+∠OAB=180°.∴点O、A、C在同一条直线.
∴∠AOB=∠C=45°,即∠CBO=90°.
在Rt△OAE中,OE=AE=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032006912391.png)
,点A的坐标为(
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032006912391.png)
,
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032006912391.png)
).
又∵B的坐标为(
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032006678336.png)
,0),∴过A、B两点的直线为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032006756555.png)
.
②当点A位于第四象限时(如图2),点A的坐标为(
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032006912391.png)
,
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032006990414.png)
),
∵B的坐标为(
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032006678336.png)
,0),∴过A、B两点的直线为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032006771523.png)
.
综上所述,过A、B两点的直线为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032006756555.png)
或
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032006771523.png)
.