File:Finding center of hyperbola.gif

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Finding_center_of_hyperbola.gif ‎(512 × 256 pixels, file size: 53 KB, MIME type: image/gif, looped, 12 frames, 9.6 s)

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Description
English: How to geometrically find the center of a hyperbola:

1. Take two points, A and B, on the same piece of the hyperbola
2. Take another point, A', on the hyperbola
3. Draw a line through A', parallel to AB
4. Let the other intersection of the new line and the hyperbola be B'
5. Let M be the midpoint of [AB] and M' the midpoint of [A'B']
6. Let I and I' be the intersections of the hyperbola with MM'

7. The center, O, is the midpoint of [II']
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Source Own work
Author Alkados
Permission
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Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

This method also works for ellipses.
Step 1 from the description requires points A and B to lie on the same piece because otherwise, MM' would not intersect the hyperbola for step 6.

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current03:01, 16 May 2010Thumbnail for version as of 03:01, 16 May 2010512 × 256 (53 KB)Alkados (talk | contribs){{Information |Description={{en|1=How to geometrically find the center of a hyperbola:<br> 1. Take two points on the hyperbola, A and B<br> 2. Take another point, A', on the hyperbola<br> 3. Draw a line through A', parallel to AB<br> 4. Let the other inte

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