x²/m+y²/[m/(m+3)]=1
是椭圆则m>0,m/(m+3)>0
所以m>0
m-m/(m+3)=(m²+2m)/(m+3)=m(m+2)/(m+3)>0
m>m/(m+3)
所以焦点在x轴
a²=m,b²=m/(m+3)
c²=a²-b²=(m²+2m)/(m+3)
e²=c²/a²=(m+2)/(m+3)=1-1/(m+3)
a²=m=(e²-2)/(1-e²)
b²=m/(m+3)=(e²-2)/(1-2e²)
所以长轴=2a=2√[(e²-2)/(1-e²)]
短轴=2b=2√[(e²-2)/(1-2e²)]
焦点{-√[(m²+2m)/(m+3)],0},{√[(m²+2m)/(m+3)],0}
顶点{-√[(e²-2)/(1-e²)],0},{√[(e²-2)/(1-e²)].0},{0,-√[(e²-2)/(1-2e²)]},{0,-√[(e²-2)/(1-2e²)]}