{"id":8341,"date":"2025-04-25T10:00:00","date_gmt":"2025-04-25T03:00:00","guid":{"rendered":"https:\/\/example.com\/?p=8341"},"modified":"2025-04-28T11:47:49","modified_gmt":"2025-04-28T04:47:49","slug":"matematika-kelas-11-pengertian-dan-persamaan-lingkaran","status":"publish","type":"post","link":"https:\/\/staging-blog.sirogu.com\/blog\/matematika-kelas-11-pengertian-dan-persamaan-lingkaran","title":{"rendered":"Cara Menentukan Persamaan Lingkaran dan Contohnya | Matematika Kelas 11"},"content":{"rendered":"<p style=\"text-align: justify;\"><img decoding=\"async\" class=\"aligncenter size-medium\" src=\"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/38aaa453-72e2-4100-8e7c-726734a4ab83.png\" alt=\"persamaan lingkaran\" \/><\/p>\n<blockquote>\n<p style=\"text-align: center;\"><em><strong><a href=\"https:\/\/www.ruangguru.com\/blog\/c\/matematika\/matematika-sma-kelas-11\">Artikel Matematika kelas 11<\/a><\/strong> kali ini akan menjelaskan tentang cara menentukan persamaan lingkaran. Ingin tahu bagaimana penjelasannya? Simak artikel berikut yang juga menyajikan contoh soalnya lho.<\/em><\/p>\n<\/blockquote>\n<p style=\"text-align: center;\">&#8212;<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">Coba sekali-kali pas kamu lagi bantu-bantu cuci motor atau mobil, perhatikan bagian rodanya deh. Di mobil tuh, bagian tengah-tengah velg (logam\/kaleng yang terpasang pada ban) biasanya ada logo perusahaan yang membuat mobil tersebut. Kalau kamu perhatikan, titik tengah dari logo tersebut pasti memiliki jarak yang sama jika ditarik ke sisi-sisi luar ban yang berbentuk lingkaran.<\/p>\n<p style=\"text-align: justify;\">Nah, sebelumnya kamu sudah belajar tentang bangun datar kan. Lingkaran termasuk salah satu bentuk bangun datar lho. Hayoo, apa kamu masih ingat apa itu lingkaran?<\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" style=\"width: 600px; display: block; margin: 0px auto;\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/matematika%20kelas%2011%20-%20pengertian%20-%20persamaan%20lingkaran.png\" alt=\"matematika kelas 11 - pengertian - persamaan lingkaran\" width=\"600\" \/><\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><strong>Titik<\/strong> yang dimaksud dari pengertian tersebut ialah <strong>pusat lingkaran<\/strong>, dan <strong>jarak<\/strong> yang dimaksud ialah <strong>jari-jari<\/strong>.<\/p>\n<p style=\"text-align: justify;\">Setelah tahu pengertian lingkaran, berikut dijelaskan mengenai persamaan dan unsur lingkaran. Ada dua hal penting yang harus kamu pahami di persamaan lingkaran, yakni jari-jari dan pusat lingkaran. Ada pun kaidahnya seperti berikut:<\/p>\n<p><strong>Baca Juga: <a href=\"https:\/\/www.ruangguru.com\/blog\/pengertian-dan-unsur-unsur-lingkaran\">Unsur-Unsur Lingkaran Ada Apa Saja, Ya?<\/a><\/strong><\/p>\n<p>&nbsp;<\/p>\n<h2><span style=\"font-size: 18pt;\">Bentuk Umum Persamaan Lingkaran<\/span><\/h2>\n<p><img decoding=\"async\" class=\"aligncenter size-medium\" src=\"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/b19ff9f2-8e16-47ba-ac9d-9bac9d225df8.jpg\" alt=\"contoh lingkaran dengan titik pusat (0,0)\" width=\"400\" \/><\/p>\n<p style=\"text-align: justify;\">Jika <strong>pusatnya (0,0)<\/strong> dan <strong>jari-jari itu r<\/strong>, maka <strong>bentuk persamaannya x<sup>2<\/sup> + y<sup>2<\/sup> = r<sup>2<\/sup>.<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-medium\" src=\"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/fe12e79b-f8d8-422a-bee8-6c8065dcb06d.png\" alt=\"contoh lingkaran dengan titik pusat (a,b)\" width=\"500\" \/><\/p>\n<p style=\"text-align: justify;\">Jika <strong>pusatnya (a,b)<\/strong> dan <strong>jari-jari itu r<\/strong>, maka <strong>bentuk persamaannya (x &#8211; a)<sup>2<\/sup> + (y &#8211; b)<sup>2<\/sup> = r<sup>2<\/sup>.<\/strong><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"width: 600px; display: block; margin: 0px auto;\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/matematika%20kelas%2011%20-%20kaidah%20-%20persamaan%20lingkaran-1.png\" alt=\"matematika kelas 11 - kaidah - persamaan lingkaran-1\" width=\"600\" \/><\/p>\n<p>&nbsp;<\/p>\n<h2><span style=\"font-size: 18pt;\">Cara Mencari Titik Pusat dan Jari-Jari dari Persamaan Lingkaran<\/span><\/h2>\n<p style=\"text-align: justify;\">Nah, terus gimana nih kalau kamu ingin mencari titik pusat dan jari-jari dari persamaan lingkaran yang diketahui. Gampang banget! Kamu bisa menggunakan dua pilihan cara, yakni:<\/p>\n<p style=\"text-align: justify;\">Pertama, jika <strong>persamaannya (x &#8211; a)<sup>2<\/sup> + (y &#8211; b)<sup>2<\/sup> = r<sup>2<\/sup><\/strong>, maka <strong>pusatnya (a, b) dan jari-jarinya r<\/strong>.<\/p>\n<p style=\"text-align: justify;\">Kedua, jika <strong>persamaannya x<sup>2<\/sup> + y<sup>2<\/sup> + Ax + Bx + C = 0<\/strong>, maka <strong>pusatnya<\/strong> <img decoding=\"async\" style=\"width: 100px;\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/pusat-1.png\" alt=\"pusat-1\" width=\"100\" \/>\u00a0dan <strong>jari-jarinya<\/strong> <img decoding=\"async\" style=\"width: 120px;\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/jari-jari.png\" alt=\"jari-jari\" width=\"120\" \/>.<\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" style=\"width: 600px; display: block; margin: 0px auto;\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/matematika%20kelas%2011%20-%20menentukan%20-%20persamaan%20lingkaran.png\" alt=\"matematika kelas 11 - menentukan - persamaan lingkaran\" width=\"600\" \/><\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Baca Juga: <a href=\"https:\/\/www.ruangguru.com\/blog\/cara-menghitung-unsur-lingkaran\">Rumus Menghitung Unsur-Unsur Lingkaran dan Contohnya<\/a><\/strong><\/p>\n<p>&nbsp;<\/p>\n<h2><span style=\"font-size: 18pt;\">Contoh Soal Persamaan Lingkaran<\/span><\/h2>\n<p style=\"text-align: justify;\">Biar makin paham dengan materinya, kita latihan soal dulu, yuk! Kita kerjakan sama-sama, ya.<\/p>\n<p style=\"text-align: justify;\">Sebuah lingkaran memiliki titik pusat (2, 3) dan berdiameter 8 cm. Persamaan lingkaran tersebut adalah\u2026<\/p>\n<ol style=\"list-style-type: upper-alpha;\">\n<li style=\"text-align: justify;\">x\u00b2 + y\u00b2 &#8211; 4x &#8211; 6y &#8211; 3 = 0<\/li>\n<li style=\"text-align: justify;\">x\u00b2 + y\u00b2 + 4x &#8211; 6y &#8211; 3 = 0<\/li>\n<li style=\"text-align: justify;\">x\u00b2 + y\u00b2 &#8211; 4x + 6y &#8211; 3 = 0<\/li>\n<li style=\"text-align: justify;\">x\u00b2 + y\u00b2 + 4x + 6y + 3 = 0<\/li>\n<li style=\"text-align: justify;\">x\u00b2 + y\u00b2 + 4x &#8211; 6y + 3 = 0<\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><strong>Jawaban: A<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Pembahasan:<\/strong><\/p>\n<p style=\"text-align: justify;\">Karena d = 8, berarti r = 8\/2 = 4, sehingga persamaan lingkaran yang terbentuk adalah:<\/p>\n<p style=\"text-align: justify;\">(x &#8211; 2)\u00b2 + (y &#8211; 3)\u00b2 = 42<\/p>\n<p style=\"text-align: justify;\">x\u00b2 &#8211; 4x + 4 + y\u00b2 -6y + 9 = 16<\/p>\n<p style=\"text-align: justify;\">x\u00b2 + y\u00b2 &#8211; 4x &#8211; 6y &#8211; 3 = 0<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"width: 600px; display: block; margin: 0px auto;\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/matematika%20kelas%2011%20-%20rumus%20bantu%20-%20persamaan%20lingkaran.png\" alt=\"matematika kelas 11 - rumus bantu - persamaan lingkaran\" width=\"600\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">Gimana nih penjelasan tentang cara menentukan persamaan lingkaran? Semoga bisa membuat kamu paham ya. Kalau masih bingung, kamu nggak perlu khawatir. Belajar lebih mudah dan asyik sekarang bisa di <strong><a href=\"https:\/\/ruangguru.com\/belajar_desktop\" rel=\" noopener\">ruangbelajar for desk<\/a><a href=\"https:\/\/ruangguru.com\/belajar_desktop\">top<\/a><\/strong> lho. Install aplikasinya di laptop kamu dan tonton video belajar animasinya. Daftar sekarang juga yuk.<\/p>\n<p style=\"text-align: center;\"><a class=\"rg-cta\" style=\"text-align: center;\" href=\"https:\/\/www.ruangguru.com\/download-for-desktop\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/cta\/f51e0d89-905d-477d-b7f8-546567f121d9.jpeg\" alt=\"IDN CTA Blog ruangbelajar for desktop Ruangguru\" \/><\/a><\/p>\n<p style=\"text-align: left;\"><strong>Referensi:<\/strong><\/p>\n<p style=\"text-align: left;\">Sutrisna, Waluyo S. Konsep Penerapan Matematika SMA\/MA Kelas XI. Jakarta: Bumi Aksara.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Artikel Matematika kelas 11 kali ini akan menjelaskan tentang cara menentukan persamaan lingkaran. Ingin tahu bagaimana penjelasannya? Simak artikel berikut yang juga menyajikan contoh soalnya lho. &#8212; &nbsp; Coba sekali-kali pas kamu lagi bantu-bantu cuci motor atau mobil, perhatikan bagian rodanya deh. Di mobil tuh, bagian tengah-tengah velg (logam\/kaleng yang terpasang pada ban) biasanya ada [&hellip;]<\/p>\n","protected":false},"author":16,"featured_media":8341,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_knawatfibu_url":["https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/38aaa453-72e2-4100-8e7c-726734a4ab83.png"],"_edit_last":["1"],"_edit_lock":["1745815532:1"],"_wp_old_date":["2019-04-08"]},"categories":[467,475],"tags":[31,10,37],"class_list":["post-8341","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika","category-matematika-sma-kelas-11","tag-kelas-11","tag-konsep-pelajaran","tag-sma"],"aioseo_notices":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Cara Menentukan Persamaan Lingkaran dan Contohnya | Matematika Kelas 11 - Belajar Gratis di Rumah Kapan Pun! | Blog Ruangguru<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/staging-blog.sirogu.com\/blog\/matematika-kelas-11-pengertian-dan-persamaan-lingkaran\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Cara Menentukan Persamaan Lingkaran dan Contohnya | Matematika Kelas 11 - Belajar Gratis di Rumah Kapan Pun! | Blog Ruangguru\" \/>\n<meta property=\"og:description\" content=\"Artikel Matematika kelas 11 kali ini akan menjelaskan tentang cara menentukan persamaan lingkaran. 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Ingin tahu bagaimana penjelasannya? Simak artikel berikut yang juga menyajikan contoh soalnya lho. &#8212; &nbsp; Coba sekali-kali pas kamu lagi bantu-bantu cuci motor atau mobil, perhatikan bagian rodanya deh. Di mobil tuh, bagian tengah-tengah velg (logam\/kaleng yang terpasang pada ban) biasanya ada [&hellip;]","og_url":"https:\/\/staging-blog.sirogu.com\/blog\/matematika-kelas-11-pengertian-dan-persamaan-lingkaran","og_site_name":"Belajar Gratis di Rumah Kapan Pun! | Blog Ruangguru","article_publisher":"https:\/\/www.facebook.com\/ruanggurucom\/","article_published_time":"2025-04-25T03:00:00+00:00","article_modified_time":"2025-04-28T04:47:49+00:00","author":"Tedy Rizkha Heryansyah","twitter_card":"summary_large_image","twitter_creator":"@ruangguru","twitter_site":"@ruangguru","twitter_misc":{"Written by":"Tedy Rizkha Heryansyah","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/staging-blog.sirogu.com\/blog\/matematika-kelas-11-pengertian-dan-persamaan-lingkaran#article","isPartOf":{"@id":"https:\/\/staging-blog.sirogu.com\/blog\/matematika-kelas-11-pengertian-dan-persamaan-lingkaran"},"author":{"name":"Tedy Rizkha Heryansyah","@id":"https:\/\/staging-blog.sirogu.com\/blog\/#\/schema\/person\/b6487dbd67e3fd331419af62ec824ad2"},"headline":"Cara Menentukan Persamaan Lingkaran dan Contohnya | Matematika Kelas 11","datePublished":"2025-04-25T03:00:00+00:00","dateModified":"2025-04-28T04:47:49+00:00","mainEntityOfPage":{"@id":"https:\/\/staging-blog.sirogu.com\/blog\/matematika-kelas-11-pengertian-dan-persamaan-lingkaran"},"wordCount":437,"commentCount":0,"publisher":{"@id":"https:\/\/staging-blog.sirogu.com\/blog\/#organization"},"image":{"@id":"https:\/\/staging-blog.sirogu.com\/blog\/matematika-kelas-11-pengertian-dan-persamaan-lingkaran#primaryimage"},"thumbnailUrl":"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/38aaa453-72e2-4100-8e7c-726734a4ab83.png","keywords":["Kelas 11","Konsep Pelajaran","SMA"],"articleSection":["Matematika","Matematika SMA Kelas 11"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/staging-blog.sirogu.com\/blog\/matematika-kelas-11-pengertian-dan-persamaan-lingkaran#respond"]}]},{"@type":"WebPage","@id":"https:\/\/staging-blog.sirogu.com\/blog\/matematika-kelas-11-pengertian-dan-persamaan-lingkaran","url":"https:\/\/staging-blog.sirogu.com\/blog\/matematika-kelas-11-pengertian-dan-persamaan-lingkaran","name":"Cara Menentukan Persamaan Lingkaran dan Contohnya | Matematika Kelas 11 - Belajar Gratis di Rumah Kapan Pun! 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