{"id":1990,"date":"2015-11-12T18:30:43","date_gmt":"2015-11-12T18:30:43","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&#038;p=1990"},"modified":"2015-11-12T18:30:43","modified_gmt":"2015-11-12T18:30:43","slug":"key-concepts-glossary-21","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/chapter\/key-concepts-glossary-21\/","title":{"raw":"Key Concepts &amp; Glossary","rendered":"Key Concepts &amp; Glossary"},"content":{"raw":"<h2>Key Concepts<\/h2>\n<ul><li>Any conic may be determined by a single focus, the corresponding eccentricity, and the directrix. We can also define a conic in terms of a fixed point, the focus [latex]P\\left(r,\\theta \\right)[\/latex] at the pole, and a line, the directrix, which is perpendicular to the polar axis.<\/li>\n\t<li>A conic is the set of all points [latex]e=\\frac{PF}{PD}[\/latex], where eccentricity [latex]e[\/latex] is a positive real number. Each conic may be written in terms of its polar equation.<\/li>\n\t<li>The polar equations of conics can be graphed.<\/li>\n\t<li>Conics can be defined in terms of a focus, a directrix, and eccentricity.<\/li>\n\t<li>We can use the identities [latex]r=\\sqrt{{x}^{2}+{y}^{2}},x=r\\text{ }\\cos \\text{ }\\theta [\/latex], and [latex]y=r\\text{ }\\sin \\text{ }\\theta [\/latex] to convert the equation for a conic from polar to rectangular form.<\/li>\n<\/ul><h2>Glossary<\/h2>\n<dl id=\"fs-id2172786\" class=\"definition\"><dt>eccentricity<\/dt><dd id=\"fs-id2172791\">the ratio of the distances from a point [latex]P[\/latex] on the graph to the focus [latex]F[\/latex] and to the directrix [latex]D[\/latex] represented by [latex]e=\\frac{PF}{PD}[\/latex], where [latex]e[\/latex] is a positive real number<\/dd><\/dl><dl id=\"fs-id2172885\" class=\"definition\"><dt>polar equation<\/dt><dd id=\"fs-id1271646\">an equation of a curve in polar coordinates [latex]r[\/latex] and [latex]\\theta [\/latex]<\/dd><\/dl>","rendered":"<h2>Key Concepts<\/h2>\n<ul>\n<li>Any conic may be determined by a single focus, the corresponding eccentricity, and the directrix. We can also define a conic in terms of a fixed point, the focus [latex]P\\left(r,\\theta \\right)[\/latex] at the pole, and a line, the directrix, which is perpendicular to the polar axis.<\/li>\n<li>A conic is the set of all points [latex]e=\\frac{PF}{PD}[\/latex], where eccentricity [latex]e[\/latex] is a positive real number. Each conic may be written in terms of its polar equation.<\/li>\n<li>The polar equations of conics can be graphed.<\/li>\n<li>Conics can be defined in terms of a focus, a directrix, and eccentricity.<\/li>\n<li>We can use the identities [latex]r=\\sqrt{{x}^{2}+{y}^{2}},x=r\\text{ }\\cos \\text{ }\\theta[\/latex], and [latex]y=r\\text{ }\\sin \\text{ }\\theta[\/latex] to convert the equation for a conic from polar to rectangular form.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id2172786\" class=\"definition\">\n<dt>eccentricity<\/dt>\n<dd id=\"fs-id2172791\">the ratio of the distances from a point [latex]P[\/latex] on the graph to the focus [latex]F[\/latex] and to the directrix [latex]D[\/latex] represented by [latex]e=\\frac{PF}{PD}[\/latex], where [latex]e[\/latex] is a positive real number<\/dd>\n<\/dl>\n<dl id=\"fs-id2172885\" class=\"definition\">\n<dt>polar equation<\/dt>\n<dd id=\"fs-id1271646\">an equation of a curve in polar coordinates [latex]r[\/latex] and [latex]\\theta[\/latex]<\/dd>\n<\/dl>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-1990\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Precalculus. <strong>Authored by<\/strong>: OpenStax College. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface\">http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":276,"menu_order":5,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Precalculus\",\"author\":\"OpenStax College\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1990","chapter","type-chapter","status-publish","hentry"],"part":1978,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1990","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/users\/276"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1990\/revisions"}],"predecessor-version":[{"id":2188,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1990\/revisions\/2188"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/1978"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1990\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/media?parent=1990"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1990"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/contributor?post=1990"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/license?post=1990"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}