解,
y=2x+m
4x²+9y²=36
联立方程,整理得,
40x²+36mx+9m²-36=0
△≧0
解出,-2√10≦m≦2√10
设A(x1,y1),B(x2,y2),M(x,y)
根据韦达定理,
x1+x2=-9m/10
y1+y2=2(x1+y1)+2m
=-9m/5+2m
=m/5
x=(x1+x2)/2=-9m/20
y=(y1+y2)/2=m/10
∴x/y=-9/2
2x+9y=0
综上可得,M的轨迹方程为2x+9y=0,且-2√10≦m≦2√10.