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Joseph O'Rourke
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What do you mean by the "envelope" of the $\mathcal{E}_1$ set of ellipses?


          [![Ellipses][1]][1]
          $\mathcal{E}_1$: $a=1$; $e=0,0.1,\ldots,0.9,1$.

Added after OP change, now $\mathcal{E}$:


          [![Ellipses2][2]][2]
          $a=2$; $e=0,0.1,\ldots,a$.

What do you mean by the "envelope" of the $\mathcal{E}_1$ set of ellipses?


          [![Ellipses][1]][1]
          $\mathcal{E}_1$: $a=1$; $e=0,0.1,\ldots,0.9,1$.

What do you mean by the "envelope" of the $\mathcal{E}_1$ set of ellipses?


          [![Ellipses][1]][1]
          $\mathcal{E}_1$: $a=1$; $e=0,0.1,\ldots,0.9,1$.

Added after OP change, now $\mathcal{E}$:


          [![Ellipses2][2]][2]
          $a=2$; $e=0,0.1,\ldots,a$.
Source Link
Joseph O'Rourke
  • 150.9k
  • 36
  • 358
  • 958

What do you mean by the "envelope" of the $\mathcal{E}_1$ set of ellipses?


          [![Ellipses][1]][1]
          $\mathcal{E}_1$: $a=1$; $e=0,0.1,\ldots,0.9,1$.