抛物线y^2=4x,焦点为F(1,0),顶点(0,0)
p点(x,y)
M点[(1+x)/2,y/2]
[(1+y^2/4)/2,y/2]
设M点的轨迹方程为
Y^2=2pX
代入M点
y^2/4=2p(1+y^2/4)/2
y^2=4p(1+y^2/4)
p=y^2/(4+y^2)又y^2=4x
p=4x/(4+4x)=x/(1+x)
M点的运动轨迹方程式y^2=2x^2/(1+x)