Question

已知m∈R，直线l：和圆C：。
（1）求直线l斜率的取值范围；
（2）直线l能否将圆C分割成弧长的比值为的两段圆弧？为什么？

Answer 1

 （1）斜率的取值范围是
（2）不能将圆分割成弧长的比值为的两段弧

（1）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
（2）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