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Her soru için gerekli formüller hatırlatılarak ve analitik düzlemde çizimler yapılarak çözüm süreci detaylı şekilde gösterilmektedir."]},"endTime":2008,"title":"Çemberin Analitik İncelenmesi ve Teğet Doğrular Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Çemberin Analitik İncelenmesi","list":{"type":"unordered","items":["Geometri öğretmeni Erhan Ardıç, MEB kazanım testlerinin 62. sorusunu çözerek çemberin analitik incelenmesini ele alıyor.","Çemberin standart denkleminin bulunabilmesi için merkez noktası ve yarıçapının bilinmesi gerekiyor.","Çember denklemi, iki nokta arasındaki uzaklığın geometrik yer denklemidir ve (x-a)² + (y-b)² = r² şeklinde ifade edilir."]},"beginTime":12,"endTime":24,"href":"/video/preview/11070401013522441368?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=12&ask_summarization=1"},{"index":1,"title":"İlk Çember Sorusu","list":{"type":"unordered","items":["Verilen çember x eksenine (4,0) noktasında teğet olup, y eksenini (0,20) ve B noktalarında kesmektedir.","Çemberin merkezinden kirişe giden dik doğru yarıçap uzunluğu ile aynıdır ve kirişi iki eşit parçaya böler.","Çemberin yarıçapı 5 birim, merkezi (4,5) olduğundan denklemi (x-4)² + (y-5)² = 25 olarak bulunur."]},"beginTime":24,"endTime":196,"href":"/video/preview/11070401013522441368?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=24&ask_summarization=1"},{"index":2,"title":"İkinci Çember Sorusu","list":{"type":"unordered","items":["Bir çember belirtebilmesi için genel formatı ax² + by² + cx + cy + dx + ey + f = 0 şeklinde olmalı ve x×y teriminin sıfır olması gerekir.","Verilen denklemde x×y terimi var olduğu için b = 3 ve a = 8 olarak bulunur.","Denklem tam kare haline getirildiğinde (x+1)² + (y+2)² = 1 olarak yazılır ve çemberin yarıçapı 1 birimdir."]},"beginTime":196,"endTime":400,"href":"/video/preview/11070401013522441368?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=196&ask_summarization=1"},{"index":3,"title":"Üçüncü Çember Sorusu","list":{"type":"unordered","items":["Analitik düzlemde x² + y² + 6y - 27 = 0 denkleminin merkezi (-d/2, -e/2) formülüyle (0, -3) olarak bulunur.","Denklem tam kare haline getirildiğinde (x+y+3)² = 36 olarak yazılır ve çemberin yarıçapı 6 birimdir.","Orijinden geçen en kısa kiriş, merkezden gelen doğruya dik olan kiriştir ve uzunluğu 6 birimdir."]},"beginTime":400,"endTime":585,"href":"/video/preview/11070401013522441368?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=400&ask_summarization=1"},{"index":4,"title":"Çember Denklemi Problemi","list":{"type":"unordered","items":["Analitik düzlemde eksenlere ikinci bölgede teğet olan çemberin merkezi de doğrusu üzerindedir ve eksenleri 4 ve 6 noktalarında kestiğine göre çemberin denklemi bulunuyor.","Merkez koordinatı (-r, r) olarak belirleniyor ve benzerlik kullanılarak r değeri 12 olarak hesaplanıyor.","Çemberin denklemi (x+12)² + (y-12)² = 12² olarak bulunuyor ve cevap B şıkkı olarak belirleniyor."]},"beginTime":589,"endTime":698,"href":"/video/preview/11070401013522441368?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=589&ask_summarization=1"},{"index":5,"title":"Teğet Doğru Problemi","list":{"type":"unordered","items":["6x+8y+m=0 doğrusunun x²+y²+4x-2y-20=0 çembere teğet olması için m alabileceği değerler toplamı bulunuyor.","Çemberin yarıçapı r = 5 olarak hesaplanıyor ve merkez noktası (-2,1) olarak belirleniyor.","Noktanın doğruya olan uzaklığı formülü kullanılarak m değerleri 54 ve -46 olarak bulunuyor ve toplamları 8 olarak hesaplanıyor, cevap D şıkkı."]},"beginTime":698,"endTime":892,"href":"/video/preview/11070401013522441368?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=698&ask_summarization=1"},{"index":6,"title":"Çember ve Doğru Kesişimi Problemi","list":{"type":"unordered","items":["x²+y²+2x-8y-19=0 doğrusu çemberini A ve B noktalarında kestiğine göre AB uzunluğu bulunuyor.","Çemberin merkezi (-1,4) olarak belirleniyor ve noktanın doğruya olan uzaklığı 3 birim olarak hesaplanıyor.","Çemberin yarıçapı 6 birim olarak bulunuyor ve AB uzunluğu 6√3 birim olarak hesaplanıyor, cevap E şıkkı."]},"beginTime":892,"endTime":1053,"href":"/video/preview/11070401013522441368?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=892&ask_summarization=1"},{"index":7,"title":"Çember Problemi Çözümü","list":{"type":"unordered","items":["Çemberin merkezinden teğet gelen doğru diktir ve yarıçap uzunluğu eşittir.","Çemberin merkezinden teğete indirilen dikme, kirişin yarısına eşittir.","Verilen denklem kullanılarak noktanın doğruya olan uzaklığı hesaplanarak, kirişin uzunluğu 14 birim olarak bulunmuştur."]},"beginTime":1060,"endTime":1226,"href":"/video/preview/11070401013522441368?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=1060&ask_summarization=1"},{"index":8,"title":"Teğet Doğrunun Denklemi","list":{"type":"unordered","items":["Çemberin merkezinden teğete giden doğruya yarıçap, teğete devam eden doğruya ise normal denir.","Dik doğruların eğimlerinin çarpımı -1'e eşittir.","Verilen çemberin üzerindeki P noktasından çizilen teğetin denklemi 4y - 3x + 13 = 0 olarak bulunmuştur."]},"beginTime":1226,"endTime":1356,"href":"/video/preview/11070401013522441368?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=1226&ask_summarization=1"},{"index":9,"title":"Normalin Eksenlerle Sınırladığı Bölgenin Alanı","list":{"type":"unordered","items":["Çemberin üzerindeki (8,8) noktasından geçen normalin eksenlerle sınırladığı bölgenin alanı sorulmuştur.","Normalin eğimi hesaplanarak, doğrunun denklemi 2x + y - 12 = 0 olarak bulunmuştur.","Normalin eksenlerle sınırladığı dik üçgenin alanı 16 birim kare olarak hesaplanmıştır."]},"beginTime":1356,"endTime":1480,"href":"/video/preview/11070401013522441368?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=1356&ask_summarization=1"},{"index":10,"title":"Ortak İç Teğet Çemberler","list":{"type":"unordered","items":["Denklemi 6x - 8y + c = 0 şeklinde verilen doğru, A(5,0) ve M(3,-4) merkezli çemberlerin ortak iç teğetidir.","M merkezli çemberin yarıçapı, O merkezli çemberin yarıçapının iki katıdır.","Sorunun çözümü için c'nin alabileceği değerler toplamı hesaplanacaktır."]},"beginTime":1480,"endTime":1502,"href":"/video/preview/11070401013522441368?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=1480&ask_summarization=1"},{"index":11,"title":"Çemberlerin Ortak İç Teti Problemi","list":{"type":"unordered","items":["İki çemberin ortak iç teti, her iki çembere de teğet olan doğru olarak tanımlanıyor.","Çemberlerin merkez noktaları (0,5) ve (3,-4) olup, birinci çemberin yarıçapı r, ikinci çemberin yarıçapı 2r olarak belirtiliyor.","Noktanın doğruya olan uzaklık formülü kullanılarak r ve 2r değerleri hesaplanıyor ve c'nin alabileceği değerler toplamı 140 olarak bulunuyor."]},"beginTime":1504,"endTime":1727,"href":"/video/preview/11070401013522441368?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=1504&ask_summarization=1"},{"index":12,"title":"Çemberin Orijine En Uzak Noktasından Geçen Teğet","list":{"type":"unordered","items":["Denklemi (x+2)²+(y-4)²=5 olan çemberin orijine en uzak noktasından geçen teğetin denklemi isteniyor.","Çemberin merkezi (-2,4) ve yarıçapı √5 birim olarak belirleniyor.","Teğetin geçtiği nokta (-3,6) olarak bulunuyor ve eğimi -2 olarak hesaplanıyor, denklem y=-2x-15 olarak elde ediliyor."]},"beginTime":1727,"endTime":1887,"href":"/video/preview/11070401013522441368?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=1727&ask_summarization=1"},{"index":13,"title":"Çember Üzerindeki Noktadan Çizilen Teğetin Y Eksenini Kesme Noktası","list":{"type":"unordered","items":["Çember üzerindeki (-3,1) noktasından çizilen teğetin y eksenini hangi noktada kestiği soruluyor.","Merkezden teğete giden doğrunun eğimi -1/3 olarak hesaplanıyor ve teğetin eğimi 3 olarak bulunuyor.","Teğetin denklemi y=3x+10 olarak elde ediliyor ve y eksenini (0,10) noktasında kestiği belirleniyor."]},"beginTime":1887,"endTime":2007,"href":"/video/preview/11070401013522441368?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=1887&ask_summarization=1"}],"linkTemplate":"/video/preview/11070401013522441368?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"TEST-62 (Çemberin Analitik İncelenmesi) | Mezun Matematik Kazanim Testleri","related_orig_text":"Çemberin Analitik İncelenmesi - 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Öğretmen, çemberin denklemini bulma, çemberin yarıçapını hesaplama, çemberin doğru ile ilişkisini belirleme ve çemberin denklemini bulma gibi çeşitli örnekler üzerinden konuyu pekiştirmektedir. Video, çemberin koniklerde genel denkleminin bir parçası olduğunu da belirtmektedir."]},"endTime":620,"title":"Çemberin Genel Denklemi ve Özellikleri Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Çemberin Genel Denklemi","list":{"type":"unordered","items":["Çemberin genel denklemi, merkezi (a,b) ve yarıçapı r olan çember için x² + y² - (a+b)² + c² + dx + ey + f = 0 şeklinde yazılır.","Koniklerin genel denkleminde a ile c birbirine eşit olmak ve sıfırdan farklı olmak zorundadır, b sıfır olmak zorundadır ve d² + e² - 4f > 0 şeklinde olmalıdır.","Kapalı denklem verildiğinde yarıçap, r = 1/2√(d² + e² - 4f) formülüyle bulunur."]},"beginTime":2,"endTime":88,"href":"/video/preview/15530186403969865630?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=2&ask_summarization=1"},{"index":1,"title":"Çember Denklemleri ve Özellikleri","list":{"type":"unordered","items":["Çemberin yarıçapı sıfırdan büyük olmak zorundadır, bu nedenle d² + e² - 4f > 0 denkleminden k'nın en büyük tam sayı değeri 4'tür.","Çemberin denklemi x² + y² + mx + ny + p = 0 şeklinde yazıldığında, m+n=2 ve m=n olmalıdır.","Çemberin denklemi x² + y² + 4x - 6y - 12 = 0 şeklinde verildiğinde, yarıçap r = 5 birimdir."]},"beginTime":88,"endTime":233,"href":"/video/preview/15530186403969865630?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=88&ask_summarization=1"},{"index":2,"title":"Çember ve Doğru İlişkileri","list":{"type":"unordered","items":["Merkezi y=x doğrusu üzerinde bulunan ve x ekseni bir bölgede teğet olan çemberin denklemi (x-2)² + (y-4)² = 4 şeklinde yazılır.","Çemberin denklemi x² + y² - 4x - 8y + 4 = 0 şeklinde açılır.","Çemberin merkezi (1,-2) ve yarıçapı 5 birim olan bir çemberin, (1,1) noktasından geçen en uzun uzaklığı 3√5 birimdir."]},"beginTime":233,"endTime":434,"href":"/video/preview/15530186403969865630?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=233&ask_summarization=1"},{"index":3,"title":"Çember ve Doğru Teğetliği","list":{"type":"unordered","items":["Çemberi K ve L noktalarında kesen bir doğru için, K ve L noktaları arasındaki uzaklık 6 birimdir.","Çemberi ile aynı merkezde olan ve (-2,1) noktasından geçen çemberin denklemi (x+3/2)² + (y-1)² = 1/4 şeklinde yazılır.","Bir doğru ve bir çember denkleminin teğet olması durumunda, merkezin doğruya uzaklığı yarıçapa eşittir."]},"beginTime":434,"endTime":614,"href":"/video/preview/15530186403969865630?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=434&ask_summarization=1"}],"linkTemplate":"/video/preview/15530186403969865630?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Çemberin Analitik İncelemesi -2","related_orig_text":"Çemberin Analitik İncelenmesi - 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İçerik, çemberin tanımı ve denklemleri (standart ve genel denklem) ile başlayıp, diskriminant (Δ) kullanarak çember, nokta veya sanal çember belirleme yöntemlerini açıklamaktadır. Daha sonra çember ve doğrunun konumları (kesişen, teğet, kesişmeyen) incelenmekte ve çemberin merkezi, yarıçapı ve teğet doğrularının denklemleri hesaplanmaktadır.","Video, AYT sınavına hazırlık amacıyla hazırlanmış olup, konu anlatımı sonrası çeşitli problem çözümleri sunulmaktadır. Benzerlik, Pisagor teoremi ve doğrunun eğimi gibi konular da çember analitiği problemlerinde kullanılmaktadır."]},"endTime":1736,"title":"Çemberin Analitiği Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Çemberin Analitiği Giriş","list":{"type":"unordered","items":["Konu, MEB kitabına göre çemberin analitiğini anlatacak ve gereksiz detaylarla kafa karıştırmayacak.","Çemberin analitiği, çemberin tanımı ve denklemleri ile başlar.","Çemberin tanımı: Belli bir noktadan eşit uzaklıktaki noktaların oluşturduğu kümeye çember denir."]},"beginTime":5,"endTime":78,"href":"/video/preview/2643482616513724230?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=5&ask_summarization=1"},{"index":1,"title":"Çemberin Standart Denklemi","list":{"type":"unordered","items":["Çemberin standart denklemi: (x-a)² + (y-b)² = r², burada (a,b) merkez koordinatı ve r yarıçaptır.","Standart denklemden merkez koordinatı ve yarıçapı kolayca bulabiliriz.","Örnek: (x+2)² + (y-3)² = 100 denkleminden merkez (-2,3) ve yarıçap 10 bulunur."]},"beginTime":78,"endTime":198,"href":"/video/preview/2643482616513724230?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=78&ask_summarization=1"},{"index":2,"title":"Çemberin Genel Denklemi","list":{"type":"unordered","items":["Çemberin genel denklemi: x² + Dx + y² + Ey + F = 0 şeklinde yazılır.","Merkez koordinatı (-D/2, -E/2) ve yarıçapı √(D²/4 + E²/4 - F) olarak bulunur.","Çemberin diski (Δ) = D² + E² - 4F olarak hesaplanır ve bu değere göre çemberin durumu belirlenir."]},"beginTime":198,"endTime":288,"href":"/video/preview/2643482616513724230?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=198&ask_summarization=1"},{"index":3,"title":"Çemberin Durumları","list":{"type":"unordered","items":["Δ > 0 ise denklem bir çember belirtir.","Δ = 0 ise denklem bir nokta belirtir.","Δ \u003c 0 ise denklem sanal çember belirtir."]},"beginTime":288,"endTime":345,"href":"/video/preview/2643482616513724230?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=288&ask_summarization=1"},{"index":4,"title":"Örnekler","list":{"type":"unordered","items":["Çember denklemi için k'nın değer aralığı bulma örneği verilmiştir.","Çember belirtip belirtmediği kontrolü için x² ve y² katsayılarının eşit olması gerekir.","Nokta belirtmesi durumunda diskin sıfır olması gerektiği gösterilmiştir."]},"beginTime":345,"endTime":546,"href":"/video/preview/2643482616513724230?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=345&ask_summarization=1"},{"index":5,"title":"Çember ile Doğrunun Durumu","list":{"type":"unordered","items":["MEB kitabına göre konu, çember ile doğrunun durumu ile sonlanmaktadır."]},"beginTime":546,"endTime":559,"href":"/video/preview/2643482616513724230?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=546&ask_summarization=1"},{"index":6,"title":"Çember ve Doğrunun Konumları","list":{"type":"unordered","items":["Çember ve doğrunun birbirine göre konumlarını belirlemek için çember denklemi ve doğru denklemi kullanılır.","Doğrunun denklemi çember denklemindeki y değerini değiştirerek bulunur ve elde edilen denklemin diskriminantı (delta) incelenir.","Delta sıfırdan büyükse çember ile doğru iki noktada kesilir, sıfırsa teğet olur, sıfırdan küçükse kesişmez."]},"beginTime":757,"endTime":919,"href":"/video/preview/2643482616513724230?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=757&ask_summarization=1"},{"index":7,"title":"Çember ve Doğrunun Kesim Noktaları","list":{"type":"unordered","items":["Çember ve doğrunun kesim noktalarını bulmak için iki denklemin ortak harflerini birbirine eşitleriz.","Çember ve doğrunun kesim noktaları hem çemberin hem de doğrunun denkleminde yer alır.","Çember ve doğrunun kesim noktaları bulmak için denklem çarpanlarına ayrılır ve x değerleri bulunur."]},"beginTime":919,"endTime":1067,"href":"/video/preview/2643482616513724230?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=919&ask_summarization=1"},{"index":8,"title":"Çember ve Doğru Soru Çözümü","list":{"type":"unordered","items":["Çemberin içindeki bir noktadan geçen en kısa kiriş, o noktadan merkeze çizilen doğru parçasına dik olmalıdır.","Çemberin merkezi ve yarıçapı denkleminden bulunur.","Dik doğrunun eğimi hesaplanarak doğrunun denklemi yazılır."]},"beginTime":1067,"endTime":1269,"href":"/video/preview/2643482616513724230?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=1067&ask_summarization=1"},{"index":9,"title":"Çember Denkleminin Bulunması","list":{"type":"unordered","items":["Benzerlik bilgisi kullanılarak çemberin merkezi bulunuyor.","Çemberin yarıçapı 10 birim olarak hesaplanıyor.","Çemberin merkezi (4,4) noktası olarak belirleniyor ve denklemi (x-4)² + (y-4)² = 10² olarak bulunuyor."]},"beginTime":1270,"endTime":1380,"href":"/video/preview/2643482616513724230?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=1270&ask_summarization=1"},{"index":10,"title":"Çemberin Teğet Doğrusunun Bulunması","list":{"type":"unordered","items":["Çemberin dışında (4,-2) noktasından çembere iki teğet çizilebiliyor.","Çemberin merkezi (0,0) noktası ve yarıçapı 10 birim olarak belirleniyor.","Teğet doğrunun eğimi ve çemberin üzerindeki noktanın koordinatları kullanılarak denklem bulunuyor."]},"beginTime":1380,"endTime":1530,"href":"/video/preview/2643482616513724230?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=1380&ask_summarization=1"},{"index":11,"title":"Teğet Doğrusunun Denkleminin Çözümü","list":{"type":"unordered","items":["Denklem çözülerek a değerinin 1 veya 3 olduğu bulunuyor.","a=1 için teğet doğrusunun denklemi x-3y-10=0 olarak hesaplanıyor.","a=3 için teğet doğrusunun denklemi 3x+y-10=0 olarak bulunuyor."]},"beginTime":1530,"endTime":1705,"href":"/video/preview/2643482616513724230?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=1530&ask_summarization=1"},{"index":12,"title":"Dersin Sonu ve Öneriler","list":{"type":"unordered","items":["Çemberin analitiği konusunda zorlananlar için noktanın analitiği konusunda çalışılması öneriliyor.","Soru tahmini videoları için \"AYT soru tahminleri listesi\"ne basılması tavsiye ediliyor.","Sınava soru tahminleri ile hazırlanılması öneriliyor."]},"beginTime":1705,"endTime":1735,"href":"/video/preview/2643482616513724230?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=1705&ask_summarization=1"}],"linkTemplate":"/video/preview/2643482616513724230?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Çemberin Analitiği Konu Anlatımı +1 NET | Sinav Odakli| AYT 12.Sınıf Çemberin Analitik İncelenmesi","related_orig_text":"Çemberin Analitik İncelenmesi - Çemberin Analitiği 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teğetleri, kirişleri ve denklemleri gibi konuları ele almaktadır. İlk bölümde çemberin analitik incelenmesi testinin ilk beş sorusu çözülmekte, ikinci bölümde ise Full Yayınları'nın geometri soru bankasındaki 6-10. sorular adım adım açıklanmaktadır.","Sorular arasında çemberin denklemi, teğet uzunluğu, kiriş uzunluğu, çemberin doğrunun denklemiyle ilişkisi, çemberin x eksenini kestiği noktalar, düzgün altıgenler ve petek noktaları gibi konular yer almaktadır. Her soru için koordinat sistemi çizilerek çözüm adımları gösterilmekte ve farklı çözüm yöntemleri sunulmaktadır."]},"endTime":1141,"title":"Çemberin Analitik İncelenmesi ve Geometri Soru Bankası Çözümleri","beginTime":0}],"fullResult":[{"index":0,"title":"Çemberin Analitik İncelenmesi Testi","list":{"type":"unordered","items":["Videoda çemberin analitik incelenmesinin son testi çözülecek ve böylece full yayınlar tamamlanacak.","İlk soruda analitik düzlemde x eksenine (20,0) noktasında teğet olan ve belirli bir çemberi teğet olan çemberin denklemi verilmiş, b+r değeri sorulmuş.","Çemberin merkezi (20,b) noktasında, yarıçapı r birim ve x eksenine teğet olduğu bilgisi kullanılarak Pisagor teoremi uygulanarak r=9 bulunmuş, b=9 olduğu için b+r=18 olarak cevap verilmiş."]},"beginTime":9,"endTime":202,"href":"/video/preview/9164858778376136431?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=9&ask_summarization=1"},{"index":1,"title":"Çemberin Merkezi ve Teğet Uzunluğu","list":{"type":"unordered","items":["İkinci soruda y=8 doğrusuna teğet ve x eksenini (2,10) noktalarında kesen çemberin merkezinin koordinatları sorulmuş.","Çemberin merkezinden kirişe dikme indirildiğinde kirişi ikiye böldüğü bilgisi kullanılarak yarıçap 5 bulunmuş, merkezin koordinatları (6,3) olarak hesaplanmış.","Üçüncü soruda verilen noktadan çemberine çizilen teğet parçasının uzunluğu sorulmuş, teğet uzunluğu bulmak için verilen noktayı çemberin denkleminde yerine yazıp karekökünü almak yeterli olmuş, sonuç 4 birim olarak bulunmuş."]},"beginTime":202,"endTime":362,"href":"/video/preview/9164858778376136431?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=202&ask_summarization=1"},{"index":2,"title":"Çember ve Doğrunun Kesişimi","list":{"type":"unordered","items":["Dördüncü soruda verilen doğrusunun çemberinden ayırdığı kirişin uzunluğu sorulmuş.","Çemberin merkezi (1,-2), yarıçapı √5 olarak bulunmuş.","Doğrunun merkeze olan uzaklığı hesaplanarak, kirişin uzunluğu 3√2 birim olarak bulunmuş."]},"beginTime":362,"endTime":535,"href":"/video/preview/9164858778376136431?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=362&ask_summarization=1"},{"index":3,"title":"Son Teğet Uzunluğu Sorusu","list":{"type":"unordered","items":["Beşinci soruda verilen 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hesaplanır."]},"beginTime":881,"endTime":943,"href":"/video/preview/9164858778376136431?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=881&ask_summarization=1"},{"index":8,"title":"Düzgün Altıgen ve Çember Problemi","list":{"type":"unordered","items":["Kenar uzunluğu 1 birim olan düzgün altıgenin köşelerindeki noktalara petek noktası denir ve orijin altıgenin merkezidir.","Çemberin merkezi (-4, 2) ve yarıçapı 3 birim olarak bulunur.","Çemberin içinde 19 tane petek noktası olduğu 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Eğitmen önce çemberin tanımını yaparak, bir noktaya sabit uzaklıkta bulunan noktaların geometrik yerini çember olarak tanımlar, ardından iki nokta arasındaki uzaklık ve orta nokta formüllerini hatırlatır. Daha sonra örnek sorular üzerinden çemberin standart denkleminin nasıl yazılacağını adım adım gösterir."]},"endTime":353,"title":"Çemberin Analitik İncelenmesi Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Çemberin Analitik İncelenmesi","list":{"type":"unordered","items":["Çemberin analitik incelenmesi ikinci bölümde pembe standart denklemi ile başlanıyor.","Merkezi ve yarıçapı bilinen çemberin denklemini yazmak için iki noktanın uzaklığından yararlanılıyor.","Çember, bir noktaya sabit uzaklıkta bulunan noktaların kümesidir."]},"beginTime":1,"endTime":68,"href":"/video/preview/11833052625423580261?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=1&ask_summarization=1"},{"index":1,"title":"Çemberin Standart Denklemi","list":{"type":"unordered","items":["Çemberin denklemi yazarken iki nokta arasındaki uzaklık formülü kullanılıyor: (x-a)² + (y-b)² = r².","Burada (a,b) merkez koordinatları, r ise yarıçap uzunluğudur.","İki nokta arasındaki orta nokta formülü: (x₁+x₂)/2, (y₁+y₂)/2'dir."]},"beginTime":68,"endTime":169,"href":"/video/preview/11833052625423580261?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=68&ask_summarization=1"},{"index":2,"title":"Çember Denklemlerinin Çözümü","list":{"type":"unordered","items":["Merkezi (2,3) ve yarıçapı 4 olan çemberin standart denklemi (x-2)² + (y-3)² = 16'dır.","Merkezi (0,3) ve yarıçapı 1 olan çemberin standart denklemi x² + (y-3)² = 1'dir.","Merkezi (4,2) ve yarıçapı 3 olan çemberin standart denklemi (x-4)² + (y-2)² = 9'dur.","Merkezi (0,4) ve yarıçapı 1 olan çemberin standart denklemi x² + (y-4)² = 1'dir.","Merkezi (2,3) ve yarıçapı 3 olan çemberin standart denklemi x² + (y-2)² = 9'dur.","Merkezi (-2,4) ve yarıçapı 1 olan çemberin standart denklemi (x+2)² + (y-4)² = 1'dir.","Merkezi (-1,-3) ve yarıçapı 2 olan çemberin standart denklemi (x+1)² + (y+3)² = 4'tür."]},"beginTime":169,"endTime":352,"href":"/video/preview/11833052625423580261?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=169&ask_summarization=1"}],"linkTemplate":"/video/preview/11833052625423580261?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Çemberin analitik incelenmesi (2. bölüm) -12. sınıf 4. fasikül sayfa 58","related_orig_text":"Çemberin Analitik İncelenmesi - 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Sınıf Matematik videolarına devam ediyoruz! Emrah Hoca ile birlikte 12. sınıf konularını en iyi şekilde öğrenip 2022 YKS 'ye bomba gibi hazırlanacağız! Bu dersimizde Çemberin Analitik...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3149972/b79bfe588509be508f5703504a19105a/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/8Dn1-wEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"34","reqid":"1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=videoid:17444193843764306098","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik öğretmeninin 12. sınıf öğrencilerine yönelik hazırladığı eğitim içeriğidir. Öğretmen, AYT sınavına hazırlık kapsamında çemberin analitik incelenmesi konusunu anlatmaktadır.","Video, çemberin tanımı ve standart denkleminin oluşturulması ile başlayıp, çemberin genel denklemi, merkezi ve yarıçapının bulunması yöntemlerini detaylı olarak ele almaktadır. Öğretmen, çemberin farklı konumlarındaki denklemlerini (merkezi orijinde olan, x ekseni üzerinde olan, y ekseni üzerinde olan ve her iki eksende teğet olan çemberler) açıklamakta ve çeşitli örnek sorular çözmektedir.","Videoda ayrıca çemberin teğet değme noktasına uzaklığı, çemberin eksenleri kestiği noktalar arasındaki uzaklık kullanılarak yarıçap hesaplaması, Pisagor bağıntısı ve özel üçgenler (3-4-5, 7-24-25 gibi) kullanarak yarıçap bulma yöntemleri de anlatılmaktadır. Video, çemberin analitiği konusunun ikinci derste devam edeceği bilgisiyle sonlanmaktadır."]},"endTime":1717,"title":"12. Sınıf Matematik: Çemberin Analitik İncelenmesi","beginTime":0}],"fullResult":[{"index":0,"title":"Çemberin Analitik İncelenmesi Konusuna Giriş","list":{"type":"unordered","items":["12. sınıf öğrencileri için çemberin analitik incelenmesi konusu anlatılacak.","Limit, türev ve integral kampı tamamlandıktan sonra çember analitiği videoları çekilecek.","AYT sınavında çember analitiği ile ilgili sorular gelmektedir."]},"beginTime":0,"endTime":56,"href":"/video/preview/17444193843764306098?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=0&ask_summarization=1"},{"index":1,"title":"Çemberin Tanımı ve Özellikleri","list":{"type":"unordered","items":["Çember, düzlemde bir noktaya eşit uzaklıkta olan noktaların kümesidir.","Çemberin sabit noktasına merkez, merkezden çemberin üzerindeki bir noktaya çizilen uzunluğa yarıçap denir.","İki yarıçapın bir araya gelmesiyle çap meydana gelir."]},"beginTime":56,"endTime":113,"href":"/video/preview/17444193843764306098?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=56&ask_summarization=1"},{"index":2,"title":"Çemberin Standart Denklemi","list":{"type":"unordered","items":["Çemberin standart denklemi, merkezi (a,b) noktasında ve yarıçapı r olan çember için (x-a)² + (y-b)² = r² şeklinde yazılır.","Bu denklem analitik geometrideki uzaklık formülünden türetilmiştir.","Örnek olarak merkezi (2,-5) ve yarıçapı 3 olan çemberin standart denklemi (x-2)² + (y+5)² = 9 olarak bulunur."]},"beginTime":113,"endTime":224,"href":"/video/preview/17444193843764306098?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=113&ask_summarization=1"},{"index":3,"title":"Çemberin Standart Denkleminin Uygulamaları","list":{"type":"unordered","items":["Merkezi (3,4) ve orijinden geçen, x ekseninde A noktasında ve y eksenini B noktasında kesen çemberin standart denklemi (x-3)² + (y-4)² = 25 olarak bulunur.","Çemberde merkezden kirişe dikme çizildiğinde kirişi iki eş parçaya ayırır.","Çemberin üzerindeki C noktasının x koordinatının alabileceği değerler 7 ve -1 olarak bulunur."]},"beginTime":224,"endTime":447,"href":"/video/preview/17444193843764306098?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=224&ask_summarization=1"},{"index":4,"title":"Parabol ve Çember Kesişim Noktaları","list":{"type":"unordered","items":["İki parabolün kesişim noktalarını bulmak için denklemleri birbirine eşitlenir ve çarpanlarına ayrılır.","Kesişim noktalarının apsis değerleri (x koordinatları) -1 ve 5 olarak bulunur.","Kesişim noktalarının ordinatları (y koordinatları) 10 olarak hesaplanır ve bu noktalar aynı ordinat değerine sahiptir."]},"beginTime":453,"endTime":577,"href":"/video/preview/17444193843764306098?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=453&ask_summarization=1"},{"index":5,"title":"Çemberin Standart Denklemi","list":{"type":"unordered","items":["Çemberin çapı, kesişim noktaları arasındaki mesafedir ve bu örnekte 6 birimdir.","Çemberin merkezi, kesişim noktalarının apsis ve ordinat değerlerinin ortalamasıdır (2, 10).","Çemberin standart denklemi (x-2)² + (y-10)² = 9 olarak bulunur."]},"beginTime":577,"endTime":633,"href":"/video/preview/17444193843764306098?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=577&ask_summarization=1"},{"index":6,"title":"Çember Denklemlerinin Özel Durumları","list":{"type":"unordered","items":["Merkezi orijinde olan yarıçapı r olan çemberin standart denklemi x² + y² = r²'dir.","Merkezi x ekseni üzerinde olan çemberin standart denklemi (x-a)² + y² = r²'dir.","Merkezi y ekseni üzerinde olan çemberin standart denklemi x² + (y-b)² = r²'dir."]},"beginTime":633,"endTime":710,"href":"/video/preview/17444193843764306098?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=633&ask_summarization=1"},{"index":7,"title":"Eksenlere Teğet Çemberler","list":{"type":"unordered","items":["X eksenine teğet çemberin denklemi (x-a)² + y² = b²'dir.","Y eksenine teğet çemberin denklemi x² + (y-b)² = a²'dir.","İki eksende teğet olan çemberin denklemi, merkezin koordinatlarını yarıçap değerlerini kullanarak üretir."]},"beginTime":710,"endTime":875,"href":"/video/preview/17444193843764306098?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=710&ask_summarization=1"},{"index":8,"title":"Örnek Sorular","list":{"type":"unordered","items":["Merkezi 4x-15 doğrusu üzerinde ve analitik düzlemin dördüncü bölgesinde her iki eksende teğet olan çemberin standart denklemi (x-3)² + (y+3)² = 9'dur.","Analitik düzlemde (18,0) noktasından geçen ve y ekseninde 24'te teğet olan çemberin yarıçapı sorulmaktadır."]},"beginTime":875,"endTime":1055,"href":"/video/preview/17444193843764306098?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=875&ask_summarization=1"},{"index":9,"title":"Çemberin Yarıçapını Bulma","list":{"type":"unordered","items":["Çemberin merkezi bir bölgede kalmış olduğunda, teğet değme noktasına olan uzaklık 18 birimden daha büyük, 24 birim olarak ölçülmüştür.","Dik yamuk mantığı kullanılarak, çemberin yarıçapı (r) 24 ve 18 birimlik kenarlarla birlikte Pisagor bağıntısı ile hesaplanmıştır.","3-4-5 üçgeninin katı olan 7-24-25 üçgeni kullanılarak r uzunluğu 25 birim olarak bulunmuştur."]},"beginTime":1058,"endTime":1241,"href":"/video/preview/17444193843764306098?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=1058&ask_summarization=1"},{"index":10,"title":"Çemberin Yarıçapını Bulma Örneği","list":{"type":"unordered","items":["Diordinat düzleminde y eksenini iki eş parçaya ayıran, x eksenini iki farklı noktada ve y eksenini tek noktada kesen bir çemberin yarıçapı sorulmuştur.","Çemberin merkezi y = -x + 18 doğrusu üzerinde olduğundan, merkez koordinatları (r, 18 - r) olarak belirlenmiştir.","6-8-10 üçgeni kullanılarak r uzunluğu 10 birim olarak bulunmuştur."]},"beginTime":1241,"endTime":1411,"href":"/video/preview/17444193843764306098?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=1241&ask_summarization=1"},{"index":11,"title":"Çemberin Genel Denklemi","list":{"type":"unordered","items":["Çemberin standart denklemi (x-a)² + (y-b)² = r² olarak verilmiş, bu denklem açılarak genel denkleme geçiş yapılmıştır.","Genel denklem x² + y² + dx + ey + f = 0 şeklinde elde edilmiştir.","Merkez koordinatları (-d/2, -e/2) olarak bulunmuş, yarıçap uzunluğu ise √(d² + a² - 4f) formülüyle hesaplanmıştır."]},"beginTime":1411,"endTime":1578,"href":"/video/preview/17444193843764306098?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=1411&ask_summarization=1"},{"index":12,"title":"Çemberin Merkezi ve Yarıçapı","list":{"type":"unordered","items":["Çemberin genel denklemi tam kareye tamamlanarak standart denkleme dönüştürülür.","Çemberin merkezi (-d/2, -e/2) formülüyle bulunur ve bu örnekte (-3,6) olarak hesaplanır.","Yarıçap, 1/2 çarpı karekök içinde d² + e² - 4f formülüyle hesaplanır ve bu örnekte 2 olarak bulunur."]},"beginTime":1582,"endTime":1640,"href":"/video/preview/17444193843764306098?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=1582&ask_summarization=1"},{"index":13,"title":"Çemberin Denkleminin Çözümü","list":{"type":"unordered","items":["Çemberin denklemi, x² + 6x + y² - 12y + 45 = 0 şeklinde yazılabilir.","Denklem, (x+3)² + (y-6)² = 4 şeklinde standart formuna dönüştürülebilir.","Bu dönüşümde, (x+3)² ve (y-6)² ifadeleri çemberin yarıçapını, -3 ve -6 değerleri ise merkez noktasının apsisi ve ordinatını verir."]},"beginTime":1640,"endTime":1696,"href":"/video/preview/17444193843764306098?parent-reqid=1751588831501160-6817770689301909058-balancer-l7leveler-kubr-yp-klg-27-BAL&text=%C3%87emberin+Analitik+%C4%B0ncelenmesi+-+%C3%87emberin+Analiti%C4%9Fi+-4&where=all&t=1640&ask_summarization=1"},{"index":14,"title":"Dersin Özeti","list":{"type":"unordered","items":["Bu derste standart denklemli çemberin genel denklemi arasındaki ilişki ve bunların anlamları öğrenilmiştir.","Çemberin analitiği konusu ikinci derste devam 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