若c≠0,则直线ax+by+c=o与圆x^2+y^2+ax+by+c=o的交点个数为

题目

若c≠0,则直线ax+by+c=o与圆x^2+y^2+ax+by+c=o的交点个数为

答案

ax+by+c=0
ax=-c-by
x=-(c+by)/a
[-(c+by)/a]^2+y^2+a[-(c+by)/a]+by+c=0
[-(c+by)/a]^2+y^2=0
(c+by)^2+(ay)^2=0
c^2+2bcy+(by)^2+(ay)^2=0
(a^2+b^2)y^2+2bcy+c^2=0
△=4(bc)^2-4(a^2+b^2)c^2
=-4a^2<0
所以无交点