过D(1,0)弦AB直线方程
y=k(x-1)
x^2/9+y^2/4=1
4x^2+9k^2(x-1)^2-36=0
(4+9k^2)x^2-18k^2x+9k^2-36=0
x1+x2=18k^2/(4+9k^2)
y1+y2=k(x1+x2)-2k=18k^3/(4+9k^2)-2k=-8k/(4+9k^2)
Mx=(x1+x2)/2=9k^2/(4+9K^2)
My=-4k/(4+9k^2)
M(x,y)
4x/(-9y)=k
y=-4*(4x/(-9y))/(4+9*(4x/(-9y))^2)
y=-4x*(-9y)/(81y^2+9x)
=36xy/(81y^2+9x)
1=36x/(81y^2+9x)
81y^2+9x=36x
9y^2=3x
轨迹方程 y^2=x/3 (-3