On the curve related to the locus of foci of a conic if its four tangents are given

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12410%2F18%3A43898414" target="_blank" >RIV/60076658:12410/18:43898414 - isvavai.cz</a>
Result on the web
<a href="https://2018.csgg.cz/files/csgg_2018.pdf" target="_blank" >https://2018.csgg.cz/files/csgg_2018.pdf</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
On the curve related to the locus of foci of a conic if its four tangents are given
Original language description
There exists at most one point, called Miquel point, such that feet of perpendiculars from it to the four lines are collinear. It is possible to construct a parabola with the focus at the Miquel point such that the line joining the feet of perpendiculars is its tangent at the vertex. From properties of a parabola it follows that these four lines are tangents of the parabola. This immediately brings us to the question: What is the locus of foci of remaining conics, to which the four lines are tangents? The solution is based on property inherent to any conic. Feet of perpendiculars from a focus to tangents of the conic lie on the principal circle of the conic.
Czech name
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Czech description
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Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Proceedings of the Czech-Slovak conference on Geometry and Graphics 2018
ISBN
978-80-8208-005-9
ISSN
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e-ISSN
neuvedeno
Number of pages
10
Pages from-to
41-50
Publisher name
Vydavatelstvo SCHK
Place of publication
Bratislava
Event location
Blansko
Event date
Sep 10, 2018
Type of event by nationality
EUR - Evropská akce
UT code for WoS article
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