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One focus of circumconic

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  • Steve Sigur
    This resumes an old topic. If one focus of a circumconic is known, there are 4 circumconics with that focus. This is equivalent to constructing a circumconic
    Message 1 of 1 , Jul 29, 2006
      This resumes an old topic.

      If one focus of a circumconic is known, there are 4 circumconics with
      that focus.

      This is equivalent to constructing a circumconic given 3 point on it
      and one focus.

      I learned this from the AbraCadaBri site (in French), linked below.

      Take the three known points (we will call them A, B, C) and draw
      circles centered at these points through F, the known focus.

      These circles have, two by two, 6 centers of similarity (where the
      internal and external tangents meet) which lie on 4 lines. Each of
      these lines is a directrix which gives the construction of each conic.

      Also the external tangents of two nearby circles through F and
      centered at points on the conic meet on a directrix.

      Steve

      Abracadabri site
      http://www-cabri.imag.fr/abracadabri/Coniques/MonoFocale/ExoD3pt.html

      Notation:
      http://paideiaschool.org/TeacherPages/Steve_Sigur/resources/VoodooPad%
      20web/notation.html


      Triangle web page:
      http://paideiaschool.org/TeacherPages/Steve_Sigur/geometryIndex.htm

      Other math:
      http://paideiaschool.org/TeacherPages/Steve_Sigur/interesting2.htm





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