动椭圆的包络线

葡萄糖

焦点在同一坐标轴上，中心在原点，椭圆周长为定值的椭圆的包络线

补充内容 (2014-6-25 13:55):
椭圆的周长为\[C=4aE\left( e \right)\]

葡萄糖

椭圆的周长为\begin{gathered}
  C = 4a\int_0^{\frac{\pi }{2}} {\sqrt {1 - {{\left( {\frac{c}{a}} \right)}^2}{{\sin }^2}\theta } d\theta }  = 4a\int_0^{\frac{\pi }{2}} {\sqrt {1 - {e^2}{{\sin }^2}\theta } d\theta }  \\
   = 4a\int_0^1 {\sqrt {\frac{{1 - {{\left( {\frac{c}{a}} \right)}^2}{t^2}}}{{1 - {t^2}}}} dt}  = 4a\int_0^1 {\sqrt {\frac{{1 - {e^2}{t^2}}}{{1 - {t^2}}}} dt}  = 4aE\left( {\frac{c}{a}} \right) = 4aE\left( e \right) \\
\end{gathered}
那么能用软件解决\(椭圆的包络线\)这个问题吗？