Timeline for Will a ball fired through a focus of an ellipse eventually tend to a horizontal line?
Current License: CC BY-SA 2.5
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 21, 2011 at 20:13 | comment | added | David E Speyer | You can figure out what $c$ is by looking at the action on the tangent spaces at $0$ and $\infty$. Let the distance between the focii be $2a$ and let $R$ be the major radius. Then going through the first focus, as a map from the tangent space at $0$ to the tangent space at $\infty$, is dilation by $(R+a)/(R-a)$. Going back from $\infty$ to $0$ is dilation by that factor again. So $c=(R+a)^2/(R-a)^2$. | |
| Mar 21, 2011 at 19:10 | history | edited | zeb | CC BY-SA 2.5 |
I'm stupid; deleted 11 characters in body
|
| Mar 21, 2011 at 18:21 | history | answered | zeb | CC BY-SA 2.5 |