Question

已知集合A={(x,y)/ y-3/x-2=a+1},集合B={(x,y)/ (a^2-1)x-(a-1)y=15,a不

Answer 1

集合A={(x,y)|(y-3)/(x-2)=a+1},集合B={(x,y)| (a^2-1)x-(a-1)y=15,a≠±1},

A∩B≠空集,

{(a+1)x-y=2a-1,x≠2,

{(a^2-1)x-(a-1)y=15,a≠±1,

有解,

而(a^2-1)/(a+1)=(a-1)/1,

两直线平行或重合,

∴15/(2a-1)=a-1,

∴2a^2-3a-14=0,

解得a=-2,或7/2.