Question

hxiaoeng 已知定点B（3,0）,点A在圆X2+Y2=1上运动,M是线段AB上的一点,且AM=1\3MB,则点MR

Answer 1

C正确

设A(x0,y0),M(x,y)

x=(x0+1/3*3)/(1+1/3)=3/4(x0+1),x0=4/3*(x-3/4)

y=(y0+1/3*0)/(1+1/3)=3/4x0,y0=4/3y

A在圆X²+Y²=1 上,x0^2+y0^2=1

[4/3*(x-3/4)]^2+[4/3y]^2=1

(X-3/4)²+Y²=9/16