(本小题满分10分)
已知圆

与直线

相切于点

,且圆心在直线

上.
(Ⅰ)求圆

的方程;
(Ⅱ)设直线

与圆

相交于


两点,

是坐标原点.求

的面积最大值,并求取得最大值时直线

的方程.
解:(Ⅰ)

.
(Ⅱ)

,

,

,

.
由

.
设

,则

,

,

当

,即

,

时,

,
∴
S的最大值为2,取得最大值时

.所求直线

.
另解:


.
当且仅当

即

时,

.
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