已知双曲线x^2/3-y^2=1,直线y=kx+m与双曲线交于C.D两点,且C,D两点都在以A(0,-1),的圆上
问题描述:
已知双曲线x^2/3-y^2=1,直线y=kx+m与双曲线交于C.D两点,且C,D两点都在以A(0,-1),的圆上
求M取值范围
答
联立双曲线与直线方程,得(3k^2-2)x^2+6kmx+3m^2+6=0 ··········(1)由△>0,得3k^2<m^2+2··········(2)设C(x1,y1),D(x2,y2) 由题意则有AC^2=AD^2 即x1^2+(y1+1)^2=x2^2+(y2+1)^2整理...