(2)
设
割线y=k(x+8),弦端点a(x1,y1),b(x2,y2),点在c上,所以
x1^2+y1^2-2x1+10y1+4=0.
x2^2+y2^2-2x2+10y2+4=0.
做差,(x1+x2)(x1-x2)+(y1+y2)(y1-y2)-2(x1-x2)+10(y1-y2)=0---------------(*)
点差法设中点m(x,y),x1+x2=2x,y1+y2=2y,(*)两边除以x1-x2,
注意(y1-y2)/(x1-x2)=k
(*)化为
2x+2yk-2+10k=0
x+yk+10k-2=0----------中点轨迹方程,其中k是你所引割线的斜率