Question

已知圆C：(x-1)^2+(y-2)^2=25及直线L:(2m+1)x + (m+1)y = 7m+4.证明无论m取何实

Answer 1

(2m+1)x + (m+1)y = 7m+4

m(2x+y-7)=4-x-y

2x+y-7=0

4-x-y=0

x=3

y=1

即

直线恒过（3,1）点

而

把点代入圆的左边,有

(x-1)^2+(y-2)^2=(3-1)^2+(1-2)^2=4+1=5