One focus of circumconic
- This resumes an old topic.
If one focus of a circumconic is known, there are 4 circumconics with
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.
Triangle web page:
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