Difference between revisions of "Focus of a curve"
From Encyclopedia of Mathematics
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| − | + | A point $F$ lying in the plane of the second-order curve such that the ratio of the distance of any point of the curve from $F$ to its distance from a given line (the directrix) is equal to a constant (the eccentricity). See also [[Conic sections]]. | |
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| + | The foci of a second-order curve can be defined as the points of intersection of the tangents to that curve from the [[circular points]] of the plane. This definition can also be extended to algebraic curves of order $n$. | ||
====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> M. Berger, "Geometry" , '''1–2''' , Springer (1987) pp. Chapt. 17 (Translated from French)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> J.L. Coolidge, "Algebraic plane curves" , Dover, reprint (1959) pp. 171; 180; 183; 192</TD></TR></table> | + | <table> |
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> M. Berger, "Geometry" , '''1–2''' , Springer (1987) pp. Chapt. 17 (Translated from French)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> J.L. Coolidge, "Algebraic plane curves" , Dover, reprint (1959) pp. 171; 180; 183; 192</TD></TR></table> | ||
Latest revision as of 05:43, 9 April 2023
A point $F$ lying in the plane of the second-order curve such that the ratio of the distance of any point of the curve from $F$ to its distance from a given line (the directrix) is equal to a constant (the eccentricity). See also Conic sections.
The foci of a second-order curve can be defined as the points of intersection of the tangents to that curve from the circular points of the plane. This definition can also be extended to algebraic curves of order $n$.
References
| [a1] | M. Berger, "Geometry" , 1–2 , Springer (1987) pp. Chapt. 17 (Translated from French) |
| [a2] | J.L. Coolidge, "Algebraic plane curves" , Dover, reprint (1959) pp. 171; 180; 183; 192 |
How to Cite This Entry:
Focus of a curve. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Focus_of_a_curve&oldid=11335
Focus of a curve. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Focus_of_a_curve&oldid=11335
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article