过椭圆x22+y23=1的下焦点,且与圆x2+y2-3x+y+3/2=0相切的直线的斜率是 _ .

问题描述:

过椭圆

x2
2
+
y2
3
=1的下焦点,且与圆x2+y2-3x+y+
3
2
=0相切的直线的斜率是 ___ .

∵椭圆x22+y23=1中,a2=3且b2=2,∴c=a2-b2=1,可得椭圆的下焦点为F(-1,0).设经过F且与圆x2+y2-3x+y+32=0相切的直线的斜率为k,可得切线方程为y=kx-1,即kx-y-1=0.圆x2+y2-3x+y+32=0化成标准方程,得(x-32)2+...