Question

a为何值时,圆C1:x^2+y^2-2ax+4y+(a^2-5)=0和圆C2:x^2+y^2+2x-2ay+(a^2-3

Answer 1

有四条公切线则相离,圆心距大于半径和

(x-a)^2+(y+2)^2=9

(x+1)^2+(y-a)^2=4

圆心距是d

则d^2=(a+1)^2+(-2-a)^2=2a^2+6a+5

半径和=3+2=5

所以2a^2+6a+5>5^2

a^2+3a-10>0

a2