Question

圆(x-1)^2+(y-1)^2=9,过A(2,3)作圆的任意弦,求这些弦的中点P的轨迹方程

Answer 1

圆C:(x-1)^2+(y-1)^2=9,过A(2,3)作圆的任意弦DE,

A(2,3)在园C内

C(1,1)

DE中点P(x,y)

CP⊥DE

k(CP)=(y-1)/(x-1)

k(DE)=(y-3)/(x-2)

k(CP)*k(AB)=-1

[(y-1)/(x-1)]*[(y-3)/(x-2)]=-1

弦的中点P的轨迹方程是园:(x-1.5)^2+(y-2)^2=1.25