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- == Definitions of conic sections in terms of foci == ...e]] - The locus of all points equidistant from a fixed point (i.e. the two foci are the same point).6 KB (1,003 words) - 15:47, 13 November 2024
- ...uch that the sum of the distances from <math>P</math> to two fixed [[focus|foci]] is a constant. (The equivalence of these two definitions is a non-trivia ...cular]] to the axis of the the cone, or (in the second definition) the two foci of the ellipse coincide.5 KB (892 words) - 20:52, 1 May 2021
- ...th>2006\pi</math> passes through <math>A</math> and <math>C</math> and has foci at <math>B</math> and <math>D</math>. What is the perimeter of the rectang13 KB (2,058 words) - 11:36, 4 July 2023
- ...th>2006\pi</math> passes through <math>A</math> and <math>C</math> and has foci at <math>B</math> and <math>D</math>. What is the perimeter of the rectang ...ath>l</math> and <math>w</math>. Let the axis of the ellipse on which the foci lie have length <math>2a</math>, and let the other axis have length <math>22 KB (339 words) - 12:15, 12 July 2015
- ...point]]s such that the difference between the distances to the two [[focus|foci]] is constant. It is the [[conic section]] formed by slicing two cones such666 bytes (112 words) - 09:06, 30 January 2019
- ...ints <math>C</math> that can be centers of circles must be an ellipse with foci <math>F_1</math> and <math>F_2</math> and major axis <math>20</math>. .... Then we reflect the ellipse over <math>\ell</math> to a new ellipse with foci <math>F_1'</math> and <math>F_2'</math> as shown below.12 KB (2,001 words) - 19:26, 23 July 2024
- An [[ellipse]] has [[focus | foci]] at <math>(9,20)</math> and <math>(49,55)</math> in the <math>xy</math>-pl ...ath> such that the sum of the distances between <math>P</math> and the two foci is constant. Let <math>F_1 = (9, 20)</math>, <math>F_2 = (49, 55)</math> a5 KB (982 words) - 23:57, 5 December 2024
- An ellipse has foci at <math>(9, 20)</math> and <math>(49, 55)</math> in the <math>xy</math>-pl7 KB (1,071 words) - 18:24, 23 February 2024
- The semimajor axis passes through the [[center]] and one of the [[focus|foci]] of an [[ellipse]], and is half of the [[major axis]].307 bytes (44 words) - 21:47, 5 January 2023
- ...e are two softball bats stuck in the sand. Michael recognizes these as the foci of the ellipse. The bats are <math>24</math> feet apart. Two children stand71 KB (11,749 words) - 11:39, 20 November 2024
- ...f a [[ellipse]] is the longer of its two [[axis]] and contains the [[focus|foci]] of the ellipsis.329 bytes (62 words) - 21:51, 27 February 2020
- A circle of radius <math>r</math> passes through both foci of, and exactly four points on, the ellipse with equation <math>x^2+16y^2=113 KB (2,117 words) - 11:33, 24 August 2023
- A circle of radius <math>r</math> passes through both foci of, and exactly four points on, the ellipse with equation <math>x^2+16y^2=1 ...-\sqrt{15}, 0)</math>. In order for a circle to pass through both of these foci, we must have that the center of this circle lies on the y-axis.5 KB (836 words) - 15:09, 20 June 2020
- LEMMA: Let <math>\mathcal{E}</math> be an ellipse with foci <math>A</math> and <math>B</math>, and let <math>P</math> be a point on <ma ...math>\overline{AB_0}</math> - which is just the center of the ellipse with foci <math>A</math> and <math>B_0</math>! Hence the desired locus of centers is4 KB (657 words) - 10:40, 6 November 2016
- ...e are two softball bats stuck in the sand. Michael recognizes these as the foci of the ellipse. The bats are <math>24</math> feet apart. Two children stand ...point on the [[ellipse]], <math>F_1</math> and <math>F_2</math> be the two foci of the ellipse, and <math>A</math> and <math>B</math> be two points on line3 KB (550 words) - 16:03, 7 August 2018
- ...eters be <math>p_1</math> and <math>p_2</math> and the distances from the foci to the point of intersection of the axes be <math>x_2</math> and <math>y_110 KB (1,742 words) - 01:31, 13 November 2023
- ...athcal E</math> and <math>2c</math> is the is the distance between its two foci.)15 KB (2,383 words) - 08:49, 25 June 2023
- ...athcal E</math> and <math>2c</math> is the is the distance between its two foci.) ...ath>, and <math>c</math> (where <math>c</math> is the distance between the foci of <math>\mathcal E</math>) satisfy <math>c = \sqrt{a^2 - b^2}</math>. Thus11 KB (1,858 words) - 17:33, 1 August 2022
- ...h> is on an ellipse whose center is <math>\left( 0 , 0 \right)</math> and foci are <math>\left( - 4 , 0 \right)</math> and <math>\left( 4 , 0 \right)</mat ...is on an ellipse whose center is <math>\left( 20 , 11 \right)</math> and foci are <math>\left( 20 , 10 \right)</math> and <math>\left( 20 , 12 \right)</m2 KB (342 words) - 12:21, 7 February 2023
- The minor axis of a ellipse is the shorter of its two axis and contains the foci of the ellipsis.312 bytes (61 words) - 00:10, 4 January 2023