{"id":2807,"date":"2025-08-13T18:43:30","date_gmt":"2025-08-13T18:43:30","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=2807"},"modified":"2025-10-23T18:09:32","modified_gmt":"2025-10-23T18:09:32","slug":"conics-background-youll-need-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/conics-background-youll-need-3\/","title":{"raw":"Conics: Background You'll Need 3","rendered":"Conics: Background You&#8217;ll Need 3"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li><span data-sheets-root=\"1\">Write the equation of a circle given its graph, or its center and radius<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<p data-start=\"2503\" data-end=\"2860\">If you know the center [latex](h,k)[\/latex] and radius [latex]r[\/latex], the equation is [latex](x-h)^{2}+(y-k)^{2}=r^{2}.[\/latex]<\/p>\r\n\r\n<section class=\"textbox example\" aria-label=\"Example\">\r\n<p data-start=\"2862\" data-end=\"2989\">Write the equation of the circle with center [latex](2,-5)[\/latex] and radius [latex]4[\/latex].<\/p>\r\n<p data-start=\"2991\" data-end=\"3086\">[latex]\r\n\\begin{align}\r\n(x-h)^{2}+(y-k)^{2}&amp;=r^{2}\\\\\r\n(x-2)^{2}+(y+5)^{2}&amp;=4^{2}\\\\\r\n(x-2)^{2}+(y+5)^{2}&amp;=16\r\n\\end{align}\r\n[\/latex]<\/p>\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]313912[\/ohm_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]313913[\/ohm_question]<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li><span data-sheets-root=\"1\">Write the equation of a circle given its graph, or its center and radius<\/span><\/li>\n<\/ul>\n<\/section>\n<p data-start=\"2503\" data-end=\"2860\">If you know the center [latex](h,k)[\/latex] and radius [latex]r[\/latex], the equation is [latex](x-h)^{2}+(y-k)^{2}=r^{2}.[\/latex]<\/p>\n<section class=\"textbox example\" aria-label=\"Example\">\n<p data-start=\"2862\" data-end=\"2989\">Write the equation of the circle with center [latex](2,-5)[\/latex] and radius [latex]4[\/latex].<\/p>\n<p data-start=\"2991\" data-end=\"3086\">[latex]\\begin{align}  (x-h)^{2}+(y-k)^{2}&=r^{2}\\\\  (x-2)^{2}+(y+5)^{2}&=4^{2}\\\\  (x-2)^{2}+(y+5)^{2}&=16  \\end{align}[\/latex]<\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm313912\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313912&theme=lumen&iframe_resize_id=ohm313912&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm313913\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313913&theme=lumen&iframe_resize_id=ohm313913&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":67,"menu_order":4,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":522,"module-header":"background_you_need","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2807"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/users\/67"}],"version-history":[{"count":7,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2807\/revisions"}],"predecessor-version":[{"id":4877,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2807\/revisions\/4877"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/parts\/522"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2807\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=2807"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=2807"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=2807"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=2807"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}