摘要：1． 已知.直线:和圆:． (Ⅰ)求直线斜率的取值范围, (Ⅱ)直线能否将圆分割成弧长的比值为的两段圆弧?为什么? 解:(Ⅰ)直线的方程可化为. 直线的斜率.····························································································· 2分 因为. 所以.当且仅当时等号成立． 所以.斜率的取值范围是．·········································································· 5分 (Ⅱ)不能．················································································································· 6分 由(Ⅰ)知的方程为 .其中． 圆的圆心为.半径． 圆心到直线的距离 ．·············································································································· 9分 由.得.即．从而.若与圆相交.则圆截直线所得的弦所对的圆心角小于． 所以不能将圆分割成弧长的比值为的两段弧． 12分

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