题干

已知点A的坐标为(4,1),点B(﹣7,﹣2)关于直线y=x的对称点为C.

(Ⅰ)求以A、C为直径的圆E的方程;

(Ⅱ)设经过点A的直线l与圆E的另一个交点为D,|AD|=8,求直线l的方程.

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答案(点此获取答案解析)

解:(Ⅰ)点B(﹣7,﹣2)关于直线y=x的对称点为C(﹣2,﹣7),

∵AC为直径,AC中点E的坐标为(1,﹣3),

∴圆E的半径为|AE|=5,

∴圆E的方程为(x﹣1)2+(y+3)2=25.

(Ⅱ)当直线l的斜率不存在时,易求|AD|=8,此时直线l的方程为x=4,

当直线l的斜率存在时,设l:y﹣1=k(x﹣4),

∴圆心E到直线l的距离d=

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