{"id":5759,"date":"2013-04-25T12:16:44","date_gmt":"2013-04-25T12:16:44","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=5759"},"modified":"2014-12-02T08:27:03","modified_gmt":"2014-12-02T08:27:03","slug":"conic-sections-circle-parabola-hyperbola-and-ellipse","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2013\/04\/25\/conic-sections-circle-parabola-hyperbola-and-ellipse\/","title":{"rendered":"Conic Sections: Circle, Parabola, Hyperbola, and Ellipse"},"content":{"rendered":"

Overview:\u00a0 What Is a Conic Section?<\/strong><\/p>\n

Conic sections are\u00a0the curves\u00a0formed when a right circular cone intersects with a plane.\u00a0 The angle that the plane \u00a0makes when it “cuts through” the cone determines the shape of the section.\u00a0 The four main types of conic sections are the circle, the parabola, the hyperbola, and the ellipse.<\/p>\n

The Circle Has One Fixed Center Point<\/strong><\/p>\n

The circle is the curve that is formed when the plane that intersects the cone is perpendicular to the axis of the cone.\u00a0 In other words, the plane cuts though the cone at a 900<\/sup> angle.\u00a0 The radius is exactly the same distance from the center all along the curve.\u00a0 Therefore, when it is graphed, it is a closed curve.<\/p>\n

The Ellipse Has Two Foci<\/strong><\/p>\n

The ellipse is also a closed curve.\u00a0 If is formed when the plane that intersects the cone is tilted rather than perpendicular to the axis of the curve.\u00a0 The curve is the same distance from two foci, rather than from the center.\u00a0 When it is graphed, a line drawn through the segment formed by the fixed foci will be longer than a line drawn perpendicular to it.<\/p>\n

The Parabola<\/strong><\/p>\n

The parabola is an open curve.\u00a0 It is formed when the plane that intersects the cone does not cut cleanly through the cone at the center, but cuts through it at an angle.\u00a0 It is the graph of a quadratic function. The axis of symmetry divides the parabola in half in such a way that both halves are mirror images of each other.<\/p>\n

The Hyperbola<\/strong><\/p>\n

The hyperbola is also an open curve.\u00a0 It is formed when the plane that intersects the cone is parallel to a line from the long axis of the cone.\u00a0 The open curve then formed is a branch of the hyperbola.\u00a0 It has two foci that are outside the curve formed by the hyperbola.<\/p>\n

https:\/\/schooltutoring.com\/wp-content\/uploads\/sites\/8\/2013\/04\/280px-Eccentricity_svg.png<\/a><\/p>\n

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Overview:\u00a0 What Is a Conic Section? Conic sections are\u00a0the curves\u00a0formed when a right circular cone intersects with a plane.\u00a0 The angle that the plane \u00a0makes when it “cuts through” the cone determines the shape of the section.\u00a0 The four main types of conic sections are the circle, the parabola, the hyperbola, and the ellipse. The […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2,10],"tags":[285,382,575,899,1277],"class_list":["post-5759","post","type-post","status-publish","format-standard","hentry","category-algebra","category-geometry","tag-circle","tag-conic-sections","tag-ellipse","tag-hyperbola","tag-parabola"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/5759","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=5759"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/5759\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=5759"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=5759"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=5759"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}