Question

已知m∈R，直線l：和圓C：。
（1）求直線l斜率的取值范圍；
（2）直線l能否將圓C分割成弧長的比值為的兩段圓弧？為什么？

Answer 1

 （1）斜率的取值范圍是
（2）不能將圓分割成弧長的比值為的兩段弧

（1）直線的方程可化為，
直線的斜率，······················································································ 2分
因為，
所以，當且僅當時等號成立．
所以，斜率的取值范圍是．·································································· 5分
（2）不能．··········································································································· 6分
由（Ⅰ）知的方程為
，其中．
圓的圓心為，半徑．
圓心到直線的距離
．························································································· 9分
由，得，即．從而，若與圓相交，則圓截直線所得的弦所對的圓心角小于．
所以不能將圓分割成弧長的比值為的兩段弧．············································· 12分