\u0635\u064a\u063a\u0629 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635<\/strong> \u0628\u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0627\u0644\u062f\u064a\u0643\u0627\u0631\u062a\u064a\u0629 \u0647\u064a:<\/p>\n \n \u0630\u0647\u0628:<\/p>\n \u0648<\/p>\n \u0647\u064a \u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0645\u0631\u0643\u0632 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635:<\/p>\n \u0647\u0648 \u0646\u0635\u0641 \u0627\u0644\u0642\u0637\u0631 \u0627\u0644\u0623\u0641\u0642\u064a \u0644\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635.<\/li>\n \u0647\u0648 \u0646\u0635\u0641 \u0627\u0644\u0642\u0637\u0631 \u0627\u0644\u0639\u0645\u0648\u062f\u064a \u0644\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635. <\/li>\n<\/ul>\n<\/div>\n \u0627\u0644\u0646\u0648\u0639 \u0627\u0644\u0634\u0627\u0626\u0639 \u062c\u062f\u064b\u0627 \u0645\u0646 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635 \u0647\u0648 \u0627\u0644\u0630\u064a \u064a\u0642\u0639 \u0645\u0631\u0643\u0632\u0647 \u0639\u0646\u062f \u0623\u0635\u0644 \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a\u060c \u0623\u064a \u0639\u0646\u062f \u0627\u0644\u0646\u0642\u0637\u0629 (0\u060c0). \u0648\u0644\u0647\u0630\u0627 \u0627\u0644\u0633\u0628\u0628 \u0633\u0646\u0631\u0649 \u0643\u064a\u0641\u064a\u0629 \u0625\u064a\u062c\u0627\u062f \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635 \u0627\u0644\u0630\u064a \u0645\u0631\u0643\u0632\u0647 \u0646\u0642\u0637\u0629 \u0627\u0644\u0623\u0635\u0644.<\/p>\n \u0628\u0627\u062a\u0628\u0627\u0639 \u0635\u064a\u063a\u0629 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635:<\/p>\n \n \u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635 \u0645\u062a\u0645\u0631\u0643\u0632\u064b\u0627 \u062d\u0648\u0644 \u0623\u0635\u0644 \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a\u060c \u0641\u0647\u0630\u0627 \u064a\u0639\u0646\u064a \u0630\u0644\u0643<\/p>\n \n \u0648<\/p>\n \u062a\u0633\u0627\u0648\u064a 0\u060c \u0644\u0630\u0627 \u0633\u062a\u0643\u0648\u0646 \u0645\u0639\u0627\u062f\u0644\u062a\u0643:<\/p>\n \n \u0647\u0646\u0627\u0643 \u0639\u0644\u0645\u0627\u0621 \u0631\u064a\u0627\u0636\u064a\u0627\u062a \u064a\u0633\u0645\u0648\u0646 \u0647\u0630\u0627 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0623\u064a\u0636\u064b\u0627 \u0628\u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0642\u0627\u0646\u0648\u0646\u064a\u0629 \u0623\u0648 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u062e\u0641\u0636\u0629 \u0644\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635.<\/p>\n \u0628\u0645\u062c\u0631\u062f \u0623\u0646 \u0646\u0631\u0649 \u0643\u064a\u0641 \u062a\u0628\u062f\u0648 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635\u060c \u0633\u0646\u0631\u0649 \u0645\u0627 \u0647\u064a \u0639\u0646\u0627\u0635\u0631\u0647. \u0644\u0643\u0646 \u0623\u0648\u0644\u0627\u064b\u060c \u062f\u0639\u0648\u0646\u0627 \u0646\u062a\u0630\u0643\u0631 \u0645\u0627 \u0647\u0648 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635 \u0628\u0627\u0644\u0636\u0628\u0637:<\/p>\n \u0627\u0644\u0634\u0643\u0644 \u0627\u0644\u0628\u064a\u0636\u0627\u0648\u064a \u0639\u0628\u0627\u0631\u0629 \u0639\u0646 \u062e\u0637 \u0645\u0633\u0637\u062d \u0648\u0645\u063a\u0644\u0642 \u0648\u0645\u0646\u062d\u0646\u064a \u064a\u0634\u0628\u0647 \u0625\u0644\u0649 \u062d\u062f \u0643\u0628\u064a\u0631 \u0627\u0644\u0645\u062d\u064a\u0637\u060c \u0644\u0643\u0646 \u0634\u0643\u0644\u0647 \u0623\u0643\u062b\u0631 \u0628\u064a\u0636\u0627\u0648\u064a\u0629. \u0639\u0644\u0649 \u0648\u062c\u0647 \u0627\u0644\u062e\u0635\u0648\u0635\u060c \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635 \u0647\u0648 \u0645\u0648\u0636\u0639 \u062c\u0645\u064a\u0639 \u0646\u0642\u0627\u0637 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0630\u064a \u064a\u0643\u0648\u0646 \u0645\u062c\u0645\u0648\u0639 \u0627\u0644\u0645\u0633\u0627\u0641\u0627\u062a \u0625\u0644\u0649 \u0646\u0642\u0637\u062a\u064a\u0646 \u062b\u0627\u0628\u062a\u062a\u064a\u0646 \u0623\u062e\u0631\u064a\u064a\u0646 (\u062a\u0633\u0645\u0649 \u0627\u0644\u0628\u0624\u0631\u062a\u0627\u0646 F \u0648F’) \u062b\u0627\u0628\u062a\u064b\u0627.<\/p>\n \u0625\u0630\u0646 \u0639\u0646\u0627\u0635\u0631 \u0627\u0644\u0634\u0643\u0644 \u0627\u0644\u0646\u0627\u0642\u0635 \u0647\u064a:<\/p>\n \u062a\u0631\u062a\u0628\u0637 \u0627\u0644\u0639\u0646\u0627\u0635\u0631 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629 \u0644\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635 \u0645\u0639 \u0628\u0639\u0636\u0647\u0627 \u0627\u0644\u0628\u0639\u0636. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0628\u064a\u0646\u0647\u0645\u0627 \u0645\u0647\u0645\u0629 \u062c\u062f\u064b\u0627 \u0644\u0644\u062a\u062f\u0631\u064a\u0628\u0627\u062a \u0639\u0644\u0649 \u0627\u0644\u0623\u0634\u0643\u0627\u0644 \u0627\u0644\u0646\u0627\u0642\u0635\u064a\u0629\u060c \u0644\u0623\u0646\u0647\u0627 \u0639\u0627\u062f\u0629 \u0645\u0627 \u062a\u0643\u0648\u0646 \u0636\u0631\u0648\u0631\u064a\u0629 \u0644\u062d\u0644 \u0627\u0644\u0645\u0633\u0627\u0626\u0644 \u0639\u0644\u0649 \u0627\u0644\u0623\u0634\u0643\u0627\u0644 \u0627\u0644\u0646\u0627\u0642\u0635\u064a\u0629 \u0648\u062a\u062d\u062f\u064a\u062f \u0645\u0639\u0627\u062f\u0644\u0627\u062a\u0647\u0627.<\/p>\n \u0643\u0645\u0627 \u0631\u0623\u064a\u0646\u0627 \u0623\u0639\u0644\u0627\u0647 \u0641\u064a \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635\u060c \u0641\u0625\u0646 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0645\u0646 \u0623\u064a \u0646\u0642\u0637\u0629 \u0639\u0644\u0649 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635 \u0625\u0644\u0649 \u0627\u0644\u0628\u0624\u0631\u0629 F \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0645\u0646 \u0646\u0641\u0633 \u0627\u0644\u0646\u0642\u0637\u0629 \u0625\u0644\u0649 \u0627\u0644\u0628\u0624\u0631\u0629 F’ \u062a\u0643\u0648\u0646 \u062b\u0627\u0628\u062a\u0629. \u062d\u0633\u0646\u064b\u0627\u060c \u0647\u0630\u0647 \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u062b\u0627\u0628\u062a\u0629 \u062a\u0633\u0627\u0648\u064a \u0636\u0639\u0641 \u0645\u0627 \u064a\u0642\u064a\u0633\u0647 \u0627\u0644\u0645\u062d\u0648\u0631 \u0634\u0628\u0647 \u0627\u0644\u0623\u0643\u0628\u0631. \u0648\u0628\u0639\u0628\u0627\u0631\u0629 \u0623\u062e\u0631\u0649\u060c \u0641\u0625\u0646 \u0627\u0644\u0645\u0633\u0627\u0648\u0627\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u062a\u0646\u0637\u0628\u0642 \u0639\u0644\u0649 \u0623\u064a \u0646\u0642\u0637\u0629 \u0639\u0644\u0649 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635:<\/p>\n \n \u0630\u0647\u0628<\/p>\n \n \u0648<\/p>\n \u0647\u064a \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0645\u0646 \u0627\u0644\u0646\u0642\u0637\u0629 P \u0625\u0644\u0649 \u0627\u0644\u062a\u0631\u0643\u064a\u0632 F \u0648F’ \u0639\u0644\u0649 \u0627\u0644\u062a\u0648\u0627\u0644\u064a \u0648<\/p>\n \u0647\u0648 \u0637\u0648\u0644 \u0627\u0644\u0645\u062d\u0648\u0631 \u0634\u0628\u0647 \u0627\u0644\u0628\u0624\u0631\u064a.<\/p>\n \u0644\u0630\u0644\u0643\u060c \u0628\u0645\u0627 \u0623\u0646 \u0642\u0645\u0629 \u0627\u0644\u0645\u062d\u0648\u0631 \u0627\u0644\u062b\u0627\u0646\u0648\u064a \u062a\u0642\u0639 \u0641\u064a \u0645\u0646\u062a\u0635\u0641 \u0627\u0644\u0645\u062d\u0648\u0631 \u0627\u0644\u0628\u0624\u0631\u064a \u0645\u0628\u0627\u0634\u0631\u0629\u060c \u0641\u0625\u0646 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0645\u0646\u0647 \u0625\u0644\u0649 \u0625\u062d\u062f\u0649 \u0627\u0644\u0628\u0624\u0631\u062a\u064a\u0646 \u062a\u0639\u0627\u062f\u0644 \u0637\u0648\u0644 \u0627\u0644\u0645\u062d\u0648\u0631 \u0634\u0628\u0647 \u0627\u0644\u0623\u0648\u0644\u064a (<\/p>\n \n ): <\/p>\n \u0648\u0647\u0643\u0630\u0627 \u0641\u0645\u0646 \u0627\u0644\u0645\u0645\u0643\u0646 \u0645\u0646 \u0646\u0638\u0631\u064a\u0629 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633<\/a> \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u0645\u0648\u062c\u0648\u062f\u0629 \u0628\u064a\u0646 \u0646\u0635\u0641 \u0627\u0644\u0645\u062d\u0648\u0631 \u0627\u0644\u0631\u0626\u064a\u0633\u064a \u0648\u0646\u0635\u0641 \u0627\u0644\u0645\u062d\u0648\u0631 \u0627\u0644\u062b\u0627\u0646\u0648\u064a \u0648\u0646\u0635\u0641 \u0627\u0644\u0628\u0639\u062f \u0627\u0644\u0628\u0624\u0631\u064a:<\/strong><\/p>\n \n \u062a\u0630\u0643\u0631 \u0647\u0630\u0647 \u0627\u0644\u0635\u064a\u063a\u0629 \u0644\u0623\u0646\u0647\u0627 \u0633\u062a\u0643\u0648\u0646 \u0645\u0641\u064a\u062f\u0629 \u062c\u062f\u064b\u0627 \u0644\u062d\u0633\u0627\u0628 \u0646\u062a\u0627\u0626\u062c \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0639\u0644\u0627\u0645\u0627\u062a \u0627\u0644\u062d\u0630\u0641. <\/p>\n \u0645\u0646 \u0627\u0644\u0648\u0627\u0636\u062d \u0623\u0646\u0647 \u0644\u064a\u0633\u062a \u0643\u0644 \u0627\u0644\u0623\u0634\u0643\u0627\u0644 \u0627\u0644\u0646\u0627\u0642\u0635\u064a\u0629 \u0645\u062a\u0645\u0627\u062b\u0644\u0629\u060c \u0644\u0643\u0646 \u0628\u0639\u0636\u0647\u0627 \u0623\u0643\u062b\u0631 \u0627\u0633\u062a\u0637\u0627\u0644\u0629 \u0648\u0627\u0644\u0628\u0639\u0636 \u0627\u0644\u0622\u062e\u0631 \u0623\u0643\u062b\u0631 \u0625\u0637\u0631\u0627\u0621\u064b. \u0644\u0630\u0644\u0643\u060c \u0647\u0646\u0627\u0643 \u0645\u0639\u0627\u0645\u0644 \u064a\u0633\u062a\u062e\u062f\u0645 \u0644\u0642\u064a\u0627\u0633 \u0645\u062f\u0649 \u062a\u0642\u0631\u064a\u0628 \u0634\u0643\u0644 \u0628\u064a\u0636\u0627\u0648\u064a \u0645\u0639\u064a\u0646. \u064a\u0633\u0645\u0649 \u0647\u0630\u0627 \u0627\u0644\u0645\u0639\u0627\u0645\u0644 \u0627\u0644\u0627\u0646\u062d\u0631\u0627\u0641<\/strong> \u0648\u064a\u062a\u0645 \u062d\u0633\u0627\u0628\u0647 \u0628\u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n \n \u0630\u0647\u0628<\/p>\n \n \u0647\u064a \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0645\u0646 \u0645\u0631\u0643\u0632 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635 \u0625\u0644\u0649 \u0625\u062d\u062f\u0649 \u0628\u0624\u0631\u062a\u064a\u0647<\/p>\n \u0637\u0648\u0644 \u0627\u0644\u0645\u062d\u0648\u0631 \u0634\u0628\u0647 \u0627\u0644\u0631\u0626\u064a\u0633\u064a. <\/p>\n \u0643\u0645\u0627 \u062a\u0631\u0648\u0646 \u0641\u064a \u0627\u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0633\u0627\u0628\u0642\u060c \u0643\u0644\u0645\u0627 \u0643\u0627\u0646\u062a \u0642\u064a\u0645\u0629 \u0627\u0646\u062d\u0631\u0627\u0641 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635 \u0623\u0635\u063a\u0631\u060c \u0643\u0644\u0645\u0627 \u0643\u0627\u0646 \u064a\u0634\u0628\u0647 \u0627\u0644\u062f\u0627\u0626\u0631\u0629\u060c \u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u0643\u0644\u0645\u0627 \u0643\u0627\u0646 \u0627\u0644\u0645\u0639\u0627\u0645\u0644 \u0623\u0643\u0628\u0631\u060c \u0643\u0644\u0645\u0627 \u0643\u0627\u0646 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635 \u0623\u0643\u062b\u0631 \u062a\u0633\u0637\u064a\u062d\u064b\u0627. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u062a\u062a\u0631\u0627\u0648\u062d \u0642\u064a\u0645\u0629 \u0627\u0644\u0627\u0646\u062d\u0631\u0627\u0641 \u0645\u0646 \u0635\u0641\u0631 (\u0627\u0644\u062f\u0627\u0626\u0631\u0629 \u0627\u0644\u0643\u0627\u0645\u0644\u0629) \u0625\u0644\u0649 \u0648\u0627\u062d\u062f (\u0627\u0644\u062e\u0637 \u0627\u0644\u0623\u0641\u0642\u064a)\u060c \u0648\u0643\u0644\u0627\u0647\u0645\u0627 \u063a\u064a\u0631 \u0634\u0627\u0645\u0644.<\/p>\n \n Une fois que nous avons vu toutes les propri\u00e9t\u00e9s de l’ellipse, nous allons r\u00e9soudre un probl\u00e8me d’ellipse \u00e0 titre d’exemple :<\/p>\n Pour d\u00e9terminer l’\u00e9quation d’une ellipse, nous avons besoin de la longueur du demi-axe principal, de la longueur du demi-axe secondaire et des coordonn\u00e9es de son point.<\/strong> Par cons\u00e9quent, dans ce cas, nous n’avons besoin de conna\u00eetre que l’axe semi-secondaire. Ainsi, pour calculer la longueur mesur\u00e9e par l’axe semi-secondaire, nous pouvons utiliser la relation entre l’axe semi-principal, l’axe semi-secondaire et la distance semi-focale : ” title=”Rendered by QuickLaTeX.com” height=”215″ width=”2133″ style=”vertical-align: -5px;”><\/p>\n \u0623^2=\u0628^2+\u062c^2 \u0628^2=\u0623^2-\u062c^2 \u0628=\\sqrt{a^2-c^2} = \\sqrt{5^2-4^2}=\\sqrt {9} = 3<\/p>\n \\cfrac{(x-x_0)^2}{a^2}+\\cfrac{(y-y_0)^2}{b^2} = 1\\cfrac{(x-4)^2}{5^2 }+\\cfrac{(y-(-1))^2}{3^2} = 1\\cfrac{\\bm{(x-4)^2}}{\\bm{25}}+\\cfrac{\\ \u0628 \u0645 {(\u0635 +1) ^ 2}} {\\ \u0628 \u0645 {9}} \\ \u0628 \u0645 {= 1}<\/p>\n Quelle est l’\u00e9quation de l’ellipse centr\u00e9e au point C(2,0) dont l’axe semi-principal (parall\u00e8le \u00e0 l’axe X) et l’axe secondaire mesurent respectivement 6 et 3 unit\u00e9s ? Repr\u00e9senter graphiquement ladite ellipse. <\/p>\n L’\u00e9quation de l’ellipse est la suivante :” title=”Rendered by QuickLaTeX.com” height=”208″ width=”1595″ style=”vertical-align: -20px;”><\/p>\n \\cfrac{(x-x_0)^2}{a^2}+\\cfrac{(y-y_0)^2}{b^2} = 1<\/p>\n \\cfrac{(x-2)^2}{6^2}+\\cfrac{(y-0)^2}{3^2} = 1\\cfrac{\\bm{(x-2)^2}} {\\ bm {36}} + \\ cfrac {\\ bm {y ^ 2}} {\\ bm {9}} \\ bm {= 1}<\/p>\n Calculer l’\u00e9quation de l’ellipse dont le demi-axe principal (parall\u00e8le \u00e0 l’axe des abscisses) mesure 13 unit\u00e9s, son centre est l’origine des coordonn\u00e9es et la distance de son centre \u00e0 l’un de ses foyers est de 5 unit\u00e9s. <\/p>\n Pour calculer l’\u00e9quation de l’ellipse, nous devons savoir combien de temps mesure l’axe semi-secondaire. Et, pour cela, on peut utiliser la relation math\u00e9matique qui existe entre le demi-axe principal, le demi-axe secondaire et la demi-distance focale : ” title=”Rendered by QuickLaTeX.com” height=”299″ width=”2688″ style=”vertical-align: -20px;”><\/p>\n \u0623^2=\u0628^2+\u062c^2 \u0628^2=\u0623^2-\u062c^2 \u0628=\\sqrt{a^2-c^2} = \\sqrt{13^2-5^2}=\\sqrt {144} = 12<\/p>\n \\cfrac{(x-x_0)^2}{a^2}+\\cfrac{(y-y_0)^2}{b^2} = 1\\cfrac{(x-0)^2}{13^2 }+\\cfrac{(y-0)^2}{12^2} = 1\\cfrac{\\bm{x^2}}{\\bm{169}}+\\cfrac{\\bm{y^2}} {\\\u0628\u0645{144}} \\\u0628\u0645{= 1}<\/p>\n D\u00e9terminer l’\u00e9quation de l’ellipse suivante et les coordonn\u00e9es de ses foyers : <\/p>\n Les sommets horizontaux de l’ellipse sont les points (-4,1) et (10,1). Par cons\u00e9quent, son diam\u00e8tre horizontal et son rayon sont : ” title=”Rendered by QuickLaTeX.com” height=”252″ width=”2047″ style=”vertical-align: -20px;”><\/p>\n d_h=10-(-4) =14 \u0623 =\\cfrac{14}{2} = 7<\/p>\n d_v=6-(-4) =10 \u0628 =\\cfrac{10}{2} = 5<\/p>\n C_x= \\cfrac{10+(-4)}{2} = \\cfrac{6}{2} =3 C_y= \\cfrac{6+(-4)}{2} = \\cfrac{2}{ 2} = 1 \u062c(3.1)<\/p>\n \\cfrac{(x-x_0)^2}{a^2}+\\cfrac{(y-y_0)^2}{b^2} = 1\\cfrac{(x-3)^2}{7^2 }+\\cfrac{(y-1)^2}{5^2} =1\\cfrac{\\bm{(x-3)^2}}{\\bm{49}}+\\cfrac{\\bm{( \u0635-1)^2}}{\\bm{25}} \\bm{= 1}<\/p>\n \u0623^2=\u0628^2+\u062c^2 \u062c^2=\u0623^2-\u0628^2 \u062c=\\sqrt{a^2-b^2} = \\sqrt{7^2-5^2}=\\sqrt {24}<\/p>\n \\sqrt{24}<\/p>\n C(3,1) \\bm{F\\left(3+\\sqrt{24},1}\\\u064a\u0645\u064a\u0646)} \\bm{F\\left(3-\\sqrt{24},1}\\\u064a\u0645\u064a\u0646)}<\/p>\n Calculez l’\u00e9quation de l’ellipse qui r\u00e9pond aux caract\u00e9ristiques suivantes :<\/p>\n On peut calculer la demi-focale \u00e0 partir de la focale : ” title=”Rendered by QuickLaTeX.com” height=”185″ width=”1667″ style=”vertical-align: -19px;”><\/p>\n 2\u062c = 6 \u062c=\\cfrac{6}{2} \u062c=3<\/p>\n d(P,F) + d(P,F’)= 2a 3+5= 2a 8= 2a \\cfrac{8}{2}= a 4= a<\/p>\n \u0623^2=\u0628^2+\u062c^2 \u0628^2=\u0623^2-\u062c^2 \u0628=\\sqrt{a^2-c^2} = \\sqrt{4^2-3^2}=\\sqrt {7}<\/p>\n \\cfrac{(x-x_0)^2}{a^2}+\\cfrac{(y-y_0)^2}{b^2} = 1\\cfrac{(x-0)^2}{4^2 }+\\cfrac{(y-0)^2}{\\left(\\sqrt{7}\\right)^2} =1\\cfrac{\\bm{x^2}}{\\bm{16}}+\\ \u0643\u0641\u0627\u0631\u0643 {\\ \u0628\u0645 {\u0635 ^ 2}} {\\ \u0628\u0645 {7}} \\ \u0628\u0645 {= 1} $<\/p>\n \u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0647\u0630\u0647 \u0627\u0644\u0645\u0642\u0627\u0644\u0629 \u0645\u0641\u064a\u062f\u0629 \u0644\u0643\u060c \u0641\u0645\u0646 \u0627\u0644\u0645\u0624\u0643\u062f \u0623\u0646\u0643 \u0633\u062a\u0647\u062a\u0645 \u0623\u064a\u0636\u064b\u0627 \u0628\u0635\u0641\u062d\u0627\u062a\u0646\u0627 \u0627\u0644\u062e\u0627\u0635\u0629 \u0628\u0635\u064a\u063a\u0629 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0632\u0627\u0626\u062f<\/a> \u0648\u0635\u064a\u063a\u0629 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0645\u0643\u0627\u0641\u0626<\/a> . \u0633\u062a\u062c\u062f \u0634\u0631\u062d\u0627 \u0645\u0641\u0635\u0644\u0627 \u0639\u0646 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0632\u0627\u0626\u062f \u0648\u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0645\u0643\u0627\u0641\u0626\u060c \u0645\u0639\u0627\u062f\u0644\u0627\u062a\u0647\u0645\u0627\u060c \u062e\u0635\u0627\u0626\u0635\u0647\u0645\u0627\u060c \u0623\u0645\u062b\u0644\u0629\u060c \u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629\u060c…<\/p>\n","protected":false},"excerpt":{"rendered":" \u0633\u062a\u062c\u062f \u0647\u0646\u0627 \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635 (\u0627\u0644\u0635\u064a\u063a\u0629)\u060c \u0633\u0648\u0627\u0621 \u0643\u0627\u0646 \u0627\u0644\u0623\u0635\u0644 \u0647\u0648 \u0627\u0644\u0645\u0631\u0643\u0632 \u0623\u0645 \u0644\u0627. \u0633\u062a\u062c\u062f \u0623\u064a\u0636\u064b\u0627 \u0645\u0627 \u0647\u064a \u0639\u0646\u0627\u0635\u0631 \u0627\u0644\u0634\u0643\u0644 \u0627\u0644\u0646\u0627\u0642\u0635 \u0648\u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628\u0647\u0627 \u0648\u0641\u064a\u0645 \u062a\u0633\u062a\u062e\u062f\u0645. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0631\u0624\u064a\u0629 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0648\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u0645\u062d\u0644\u0648\u0644\u0629 \u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635. \u0635\u064a\u063a\u0629 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635 \u0635\u064a\u063a\u0629 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635 \u0628\u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0627\u0644\u062f\u064a\u0643\u0627\u0631\u062a\u064a\u0629 \u0647\u064a: \u0630\u0647\u0628: \u0648 \u0647\u064a \u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0645\u0631\u0643\u0632 \u0627\u0644\u0642\u0637\u0639 …<\/p>\n![\"\\cfrac{(x-x_0)^2}{a^2}+\\cfrac{(y-y_0)^2}{b^2}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e29350c8a9f9271d7c58bb5636661eae_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n\n
![\"x_0\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-87f2a80bc63f8d7bc3df68c45a787402_l3.png\" "\\"Rendered")
<\/p>\n![\"y_0\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d37dc47669aa63f72480eae663d99287_l3.png\" "\\"Rendered")
<\/p>\n![\"C(x_0,y_0)\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a54160c9f13bae428a2471d905abd6f7_l3.png\" "\\"Rendered")
<\/p>\n<\/li>\n![\"a\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" "\\"Rendered")
<\/p>\n![\"b\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" "\\"Rendered")
<\/p>\n![\"\u0635\u064a\u063a\u0629](\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/equation-dune-ellipse.webp\")
<\/figure>\n<\/div>\n<\/span> \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635 \u0627\u0644\u0645\u062a\u0645\u0631\u0643\u0632 \u0639\u0646\u062f \u0646\u0642\u0637\u0629 \u0627\u0644\u0623\u0635\u0644<\/span><\/h3>\n
<\/p>\n<\/p>\n<\/p>\n<\/p>\n![\"\\cfrac{\\bm{x^2}}{\\bm{a^2}}+\\cfrac{\\bm{y^2}}{\\bm{b^2}}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7821573c61c10361101554eb56041901_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span> \u0639\u0646\u0627\u0635\u0631 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635<\/span><\/h2>\n
\n
![\"\u0639\u0646\u0627\u0635\u0631](\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/elements-dellipse.webp\")
<\/figure>\n<\/div>\n<\/span> \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u0639\u0646\u0627\u0635\u0631 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635<\/span><\/h3>\n
![\"d(P,F)](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7cef5996a2621318273bd54d01594941_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"d(P,F)\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6be809958050006a77cc59c5b7c32557_l3.png\" "\\"Rendered")
<\/p>\n![\"d(P,F')\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-52cd58325f7f5f8ae50bf05b32b7ed55_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/p>\n![\"\u0645\u0639\u0627\u062f\u0644\u0629](\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/relation-delements-dellipse.webp\")
<\/figure>\n<\/div>\n![\"a^2=b^2+c^2\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f07be3767557be2f8c17fc9a226a2506_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span> \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635 \u0627\u0644\u0627\u0646\u062d\u0631\u0627\u0641<\/span><\/h2>\n
![\"e](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-01e68e598b53e74e9420afdb1bf6ab66_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"c\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\u063a\u0631\u064a\u0628](\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/excentricite-dellipse.webp\")
<\/figure>\n<\/div>\n![\"0\n\n<h2](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d7cba3912f2e788be4e73f1e18c9fb21_l3.png\")
<\/span> Exemple de calcul de l’\u00e9quation de l’ellipse<\/span><\/h2>\n\n
![\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0ac0d898ef827d924f8a7972d18a3d37_l3.png\" "\\"Rendered")
<\/p>\n![\"\n\n<h2](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4c8518a77b08b28dd3989532a9c1a0bd_l3.png\")
<\/span> Probl\u00e8mes r\u00e9solus de l’\u00e9quation de l’ellipse<\/span><\/h2>\n Exercice 1<\/h3>\n
![\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1a535f3c26d0c91d21ff2802c71cb131_l3.png\" "\\"Rendered")
<\/p>\n![\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e674e398f6c61cceb56ebc7d6849b2b7_l3.png\")
\n!["\u00e9quation]("https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/centre-de-lellipse-de-lequation-a-lexterieur-de-lorigine.webp")
<\/figure>\n<\/div>\n Exercice 2<\/h3>\n
![\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bcf056c99846b69f1bf4ed5ce1e6552a_l3.png\" "\\"Rendered")
<\/p>\n![\"\n\n<div](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9e53a75087af9221fe85fa404a4045ff_l3.png\")
<\/div>\n Exercice 3<\/h3>\n
!["exercices]("https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercices-resolus-de-lequation-de-lellipse.webp")
<\/figure>\n<\/div>\n![\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-76aa999f562c86113192c06e01991927_l3.png\" "\\"Rendered")
<\/p>\n![\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0ac099c741c43ec962a36c7b2bba5d06_l3.png\" "\\"Rendered")
<\/p>\n![\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-51217c6f75e2ad233a651376f2ded0e0_l3.png\" "\\"Rendered")
<\/p>\n![\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-310ed81b139fc6b5d3902b75bed66c9b_l3.png\" "\\"Rendered")
<\/p>\n![\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1653b114c298901c587b9af56e4b0c40_l3.png\" "\\"Rendered")
<\/p>\n![\"unit\u00e9s](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6f5155fae442053fd60dec7ee847fe0f_l3.png\" "\\"Rendered")
<\/p>\n![\"\n\n<div](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7d494da27f7cde61e219586567d178c8_l3.png\")
<\/div>\n Exercice 4<\/h3>\n
\n
![\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ae016b9237aee40e4130230eb495fe6b_l3.png\" "\\"Rendered")
<\/p>\n![\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-615d5b2ccb4a343777d9d707806526ab_l3.png\" "\\"Rendered")
<\/p>\n![\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-98a1c514fb7344ec3be2558c5a559feb_l3.png\" "\\"Rendered")
<\/p>\n