{"id":154762,"date":"2022-03-25T23:53:41","date_gmt":"2022-03-25T18:23:41","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/latus-rectum-of-parabola-hyperbola-ellipse-definition-equations-examples\/"},"modified":"2023-01-02T13:17:44","modified_gmt":"2023-01-02T07:47:44","slug":"latus-rectum-of-parabola-hyperbola-ellipse-definition-equations-examples","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/latus-rectum\/","title":{"rendered":"Latus Rectum of Parabola, Hyperbola, Ellipse | Definition, Equations &#038; Examples"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/latus-rectum\/#Define_Conic_Section\" title=\"Define Conic Section\">Define Conic Section<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/latus-rectum\/#What_is_Latus_Rectum\" title=\"What is Latus Rectum?\">What is Latus Rectum?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/latus-rectum\/#Parabola\" title=\"Parabola\">Parabola<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/latus-rectum\/#Latus_Rectum_of_Parabola\" title=\"Latus Rectum of Parabola\">Latus Rectum of Parabola<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/latus-rectum\/#General_Equation_of_Parabola\" title=\"General Equation of Parabola\">General Equation of Parabola<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/latus-rectum\/#Length_of_the_Latus_Rectum_of_Parabola_Derivation\" title=\"Length of the Latus Rectum of Parabola Derivation\">Length of the Latus Rectum of Parabola Derivation<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/latus-rectum\/#Latus_Rectum_of_Parabola_Formula\" title=\"Latus Rectum of Parabola Formula\">Latus Rectum of Parabola Formula<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/latus-rectum\/#Hyperbola\" title=\"Hyperbola\">Hyperbola<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/latus-rectum\/#Latus_Rectum_of_Hyperbola\" title=\"Latus Rectum of Hyperbola\">Latus Rectum of Hyperbola<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/latus-rectum\/#Ellipse\" title=\"Ellipse\">Ellipse<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/latus-rectum\/#Definition\" title=\"Definition\">Definition<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/latus-rectum\/#Shape_of_an_Ellipse\" title=\"Shape of an Ellipse\">Shape of an Ellipse<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/latus-rectum\/#Properties\" title=\"Properties\">Properties<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/latus-rectum\/#Latus_Rectum_Examples\" title=\"Latus Rectum Examples\">Latus Rectum Examples<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Define_Conic_Section\"><\/span>Define Conic Section<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A conic section is a geometric shape that is formed when a plane intersects a cone. There are four types of conic sections: circles, ellipses, parabolas, and hyperbolas.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-154761 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/latus-rectum-of-parabola-hyperbola-ellipse-definition-equations-examples.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/latus-rectum-of-parabola-hyperbola-ellipse-definition-equations-examples.jpg?v=1648232619 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/latus-rectum-of-parabola-hyperbola-ellipse-definition-equations-examples-300x212.jpg?v=1648232619 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_Latus_Rectum\"><\/span>What is Latus Rectum?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The Latus Rectum is the chord that is drawn from the focus of an ellipse to the point where the major and minor axes intersect. It is the longest chord of the ellipse.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Parabola\"><\/span>Parabola<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A parabola is a curve in mathematics that is shaped like an upside-down U. It is created by taking a point on a plane and drawing a line from that point to each point on the plane that is a certain distance away. A parabola is always symmetrical, meaning that if you fold the curve in half, the two halves will match up perfectly.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Latus_Rectum_of_Parabola\"><\/span>Latus Rectum of Parabola<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The latus rectum is the distance from the focus to the directrix of a parabola.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"General_Equation_of_Parabola\"><\/span>General Equation of Parabola<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The general equation of a parabola is:<\/p>\n<p>y = a(x &#8211; h)2 + k<\/p>\n<p>Where:<\/p>\n<p>y is the y-coordinate of the vertex<\/p>\n<p>a is the coefficient of x2<\/p>\n<p>h is the x-coordinate of the vertex<\/p>\n<p>k is the y-coordinate of the vertex<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Length_of_the_Latus_Rectum_of_Parabola_Derivation\"><\/span>Length of the Latus Rectum of Parabola Derivation<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There is no definitive answer to this question as the length of the latus rectum of a parabola can vary depending on the equation used to calculate it. However, a rough estimate of the length of the latus rectum for a parabola can be found using the following equation:<\/p>\n<p>Latus Rectum = 2p(x_0)^2<\/p>\n<p>Where p is a constant and x_0 is the coordinate of the vertex.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Latus_Rectum_of_Parabola_Formula\"><\/span>Latus Rectum of Parabola Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The latus rectum of a parabola is a line segment that is perpendicular to the directrix and has a length equal to the distance from the focus to the parabola. The latus rectum can be found using the following formula:<\/p>\n<p>Latus Rectum = \u221a(h^2 + k^2)<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Hyperbola\"><\/span>Hyperbola<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A hyperbola is a conic section with two branches, each of which is a hyperbola. The asymptotes of a hyperbola are the lines x = \u00b1 a. The foci are at (\u00b1 c, 0). The hyperbola has the equation<\/p>\n<p>x2\/a2 \u2212 y2\/b2 = 1.<\/p>\n<p>Here a and b are the lengths of the semiaxles.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Latus_Rectum_of_Hyperbola\"><\/span>Latus Rectum of Hyperbola<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The latus rectum of a hyperbola is a line segment that connects the two foci of the hyperbola and has the same length as the major axis of the hyperbola.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Ellipse\"><\/span>Ellipse<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>An ellipse is a figure formed by two lines, called the major and minor axes, drawn from the same point and intersecting at right angles. The distance from the center of the ellipse to any point on the ellipse is called the radius.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Definition\"><\/span>Definition<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A statement that is false, but is made to appear to be true.<\/p>\n<p>An example of a false statement is &#8220;I am the best basketball player in the world.&#8221;<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Shape_of_an_Ellipse\"><\/span>Shape of an Ellipse<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>An ellipse is a two-dimensional shape that has the following properties:<\/p>\n<p>-It is symmetrical about its center.<br \/>\n-The sum of the distances from the center to any two points on the ellipse is the same.<br \/>\n-The distance from the center to any point on the ellipse is greater than the distance from that point to either of the two foci.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Properties\"><\/span>Properties<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Name Type Description<\/p>\n<p>name String The name of the origin.<\/p>\n<p>url String The URL of the origin.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Latus_Rectum_Examples\"><\/span>Latus Rectum Examples<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>1. The latus rectum of a parabola is the line segment that connects the focus of the parabola to the directrix.<\/p>\n<p>2. The latus rectum of a hyperbola is the line segment that connects the two foci of the hyperbola.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Define Conic Section A conic section is a geometric shape that is formed when a plane intersects a cone. There [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Latus Rectum of Parabola Hyperbola Ellipse","_yoast_wpseo_title":"Latus Rectum of Parabola, Hyperbola, Ellipse | Definition, Equations","_yoast_wpseo_metadesc":"Learn about latus rectum topic of maths in details explained by subject experts To know more at infinitylearn.com.","custom_permalink":"maths\/latus-rectum\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Latus Rectum of Parabola, Hyperbola, Ellipse | Definition, Equations<\/title>\n<meta name=\"description\" content=\"Learn about latus rectum topic of maths in details explained by subject experts To know more at infinitylearn.com.\" \/>\n<meta name=\"robots\" content=\"index, follow, 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