{"id":5233,"date":"2018-05-10T20:38:41","date_gmt":"2018-05-10T20:38:41","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/coreq-collegealgebra\/?post_type=chapter&#038;p=5233"},"modified":"2018-05-17T04:57:20","modified_gmt":"2018-05-17T04:57:20","slug":"why-it-matters-conic-sections","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/chapter\/why-it-matters-conic-sections\/","title":{"raw":"Why It Matters: Conic Sections*","rendered":"Why It Matters: Conic Sections*"},"content":{"raw":"What do the U.S Capitol Building in Washington, D.C., Grand Central Station in New York, and St. Paul\u2019s Cathedral in London all have in common? \u00a0Aside from being architectural marvels, each of these buildings contains a whispering gallery. \u00a0A whispering gallery is most often an oblong enclosure beneath a dome or arch. \u00a0These galleries get their name because a whisper in one part of the gallery can be heard clearly on the opposite side. \u00a0Many movies and television shows have made use of whispering galleries in their plots as the conversations of the main characters are overhead. \u00a0And tour guides at the U.S. Capitol recount a story in which John Quincy Adams used the whispering gallery to eavesdrop on conversations of other House members in the 1800s.\r\n<p style=\"text-align: center;\"><img class=\"alignnone wp-image-3926\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2017\/03\/27165749\/capitol2-300x225.jpg\" alt=\"Photo shows an external view of the U.S. Capitol Building in Washington, D.C.\" width=\"262\" height=\"196\" \/><img class=\"alignnone wp-image-3924\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2017\/03\/27162832\/station-300x200.jpg\" alt=\"Photo shows a view from inside Grand Central Station in New York City.\" width=\"295\" height=\"196\" \/><img class=\"alignnone wp-image-3925\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2017\/03\/27162927\/capitol-300x213.jpg\" alt=\"Photo shows an external view of St. Paul\u2019s Cathedral in London, England.\" width=\"275\" height=\"196\" \/><\/p>\r\n<p style=\"text-align: left;\">A whispering gallery can be produced through architecture alone, or it can be created using whispering dishes, which are large, flat dishes that reflect sound. \u00a0The key is knowing exactly where to place the dishes. \u00a0Suppose you are asked to create a whispering gallery in a room with an arch that has a width of 100 feet and a height of 40 feet. \u00a0Where can you place the whispering dishes to create the gallery?<\/p>\r\nTo answer this question, you\u2019ll need to learn about conics. \u00a0The arch represents one type of conic. \u00a0At this end of this module, you can use what you\u2019ve learned to create the whispering gallery.\r\n\r\n&nbsp;\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\nThe Ellipse\r\n<ul>\r\n \t<li>Write equations of ellipses in standard form<\/li>\r\n \t<li>Graph ellipses centered at the origin<\/li>\r\n \t<li>Graph ellipses not centered at the origin<\/li>\r\n \t<li>Solve applied problems involving ellipses<\/li>\r\n<\/ul>\r\nThe Hyperbola\r\n<ul>\r\n \t<li>Locate a hyperbola\u2019s vertices and foci<\/li>\r\n \t<li>Write equations of hyperbolas in standard form<\/li>\r\n \t<li>Graph hyperbolas centered at the origin<\/li>\r\n \t<li>Graph hyperbolas not centered at the origin<\/li>\r\n \t<li>Solve applied problems involving hyperbolas<\/li>\r\n<\/ul>\r\nThe Parabola\r\n<ul>\r\n \t<li>Graph parabolas with vertices at the origin<\/li>\r\n \t<li>Write equations of parabolas in standard form<\/li>\r\n \t<li>Graph parabolas with vertices not at the origin<\/li>\r\n \t<li>Solve applied problems involving parabolas<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;","rendered":"<p>What do the U.S Capitol Building in Washington, D.C., Grand Central Station in New York, and St. Paul\u2019s Cathedral in London all have in common? \u00a0Aside from being architectural marvels, each of these buildings contains a whispering gallery. \u00a0A whispering gallery is most often an oblong enclosure beneath a dome or arch. \u00a0These galleries get their name because a whisper in one part of the gallery can be heard clearly on the opposite side. \u00a0Many movies and television shows have made use of whispering galleries in their plots as the conversations of the main characters are overhead. \u00a0And tour guides at the U.S. Capitol recount a story in which John Quincy Adams used the whispering gallery to eavesdrop on conversations of other House members in the 1800s.<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-3926\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2017\/03\/27165749\/capitol2-300x225.jpg\" alt=\"Photo shows an external view of the U.S. Capitol Building in Washington, D.C.\" width=\"262\" height=\"196\" \/><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-3924\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2017\/03\/27162832\/station-300x200.jpg\" alt=\"Photo shows a view from inside Grand Central Station in New York City.\" width=\"295\" height=\"196\" \/><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-3925\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2017\/03\/27162927\/capitol-300x213.jpg\" alt=\"Photo shows an external view of St. Paul\u2019s Cathedral in London, England.\" width=\"275\" height=\"196\" \/><\/p>\n<p style=\"text-align: left;\">A whispering gallery can be produced through architecture alone, or it can be created using whispering dishes, which are large, flat dishes that reflect sound. \u00a0The key is knowing exactly where to place the dishes. \u00a0Suppose you are asked to create a whispering gallery in a room with an arch that has a width of 100 feet and a height of 40 feet. \u00a0Where can you place the whispering dishes to create the gallery?<\/p>\n<p>To answer this question, you\u2019ll need to learn about conics. \u00a0The arch represents one type of conic. \u00a0At this end of this module, you can use what you\u2019ve learned to create the whispering gallery.<\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<p>The Ellipse<\/p>\n<ul>\n<li>Write equations of ellipses in standard form<\/li>\n<li>Graph ellipses centered at the origin<\/li>\n<li>Graph ellipses not centered at the origin<\/li>\n<li>Solve applied problems involving ellipses<\/li>\n<\/ul>\n<p>The Hyperbola<\/p>\n<ul>\n<li>Locate a hyperbola\u2019s vertices and foci<\/li>\n<li>Write equations of hyperbolas in standard form<\/li>\n<li>Graph hyperbolas centered at the origin<\/li>\n<li>Graph hyperbolas not centered at the origin<\/li>\n<li>Solve applied problems involving hyperbolas<\/li>\n<\/ul>\n<p>The Parabola<\/p>\n<ul>\n<li>Graph parabolas with vertices at the origin<\/li>\n<li>Write equations of parabolas in standard form<\/li>\n<li>Graph parabolas with vertices not at the origin<\/li>\n<li>Solve applied problems involving parabolas<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n","protected":false},"author":160,"menu_order":1,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-5233","chapter","type-chapter","status-publish","hentry"],"part":876,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/5233","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/wp\/v2\/users\/160"}],"version-history":[{"count":2,"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/5233\/revisions"}],"predecessor-version":[{"id":5235,"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/5233\/revisions\/5235"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/876"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/5233\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/wp\/v2\/media?parent=5233"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=5233"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/wp\/v2\/contributor?post=5233"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/wp\/v2\/license?post=5233"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}