## One focus of circumconic

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• 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.

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

Notation:
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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