Найдите координаты центра окружности, если ее уравнение х2 + у2 + 6х

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Найдите координаты центра окружности, если ее уравнение
х2 + у2 + 6х - 8у + 5 = 0

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zinaidazina Х² + у² + 6х - 8у + 5 = 0
Группируем
(х² + 6х) + (у²-8у) = - 5
Дополняем до квадрата суммы и квадрата разности
(х² + 6х + 9 - 9) + (у² - 8у + 16 - 16) = - 5
(х² + 6х + 9) - 9 + (у² - 8у + 16) - 16 = - 5
(х² + 6х + 9) + (у² - 8у + 16) = - 5 + 9 + 16
(х+3)² + (у-4)² = 20
(х+3)² + (у-4)² = (√20)² = уравнение данной окружности, где
О(- 3; 4) - координаты центра окружности
R = √20 = 2√5 - радиус
Ответ: (- 3; 4)

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