Quiz — Lycée Pilote Ariana - Conique.pdf

Question 1 sur 10 20:00

[{"id":18809,"question":"Quelle est l'équation cartésienne standard d'une ellipse centrée à l'origine avec un grand axe de longueur 2a et un petit axe de longueur 2b ?","option_a":"A. x²\/a² + y²\/b² = 1","option_b":"B. x²\/a² - y²\/b² = 1","option_c":"C. y² = 4ax","option_d":"D. x² + y² = a²","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation standard d'une ellipse centrée à l'origine est x²\/a² + y²\/b² = 1, où a et b sont les demi-axes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. x²\/a² + y²\/b² = 1\", \"b\": \"B. x²\/a² - y²\/b² = 1\", \"c\": ","_debug_options_count":4},{"id":18810,"question":"Une parabole a toujours une excentricité égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, l'excentricité d'une parabole est toujours égale à 1, ce qui la distingue des autres coniques.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":18811,"question":"Quelle conique est représentée par l'équation x² - 4y² = 16 après simplification ?","option_a":"A. Ellipse","option_b":"B. Hyperbole","option_c":"C. Parabole","option_d":"D. Cercle","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant par 16, on obtient x²\/16 - y²\/4 = 1, qui est l'équation standard d'une hyperbole.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. Ellipse\", \"b\": \"B. Hyperbole\", \"c\": \"C. Parabole\", \"d\": \"D. Ce","_debug_options_count":4},{"id":18812,"question":"Quel est le foyer d'une parabole d'équation y = ax² + bx + c ?","option_a":"A. (0, 1\/(4a))","option_b":"B. (-b\/(2a), (1 - b²)\/(4a) + c)","option_c":"C. (b\/(2a), c - b²\/(4a))","option_d":"D. (0, c)","option_e":"","option_f":"","bonne_reponse":"c","explication":"Pour une parabole y = ax² + bx + c, le foyer est situé en (b\/(2a), c - b²\/(4a) + 1\/(4a)).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. (0, 1\/(4a))\", \"b\": \"B. (-b\/(2a), (1 - b²)\/(4a) + c)\", \"c\": \"C","_debug_options_count":4},{"id":18813,"question":"L'excentricité d'une ellipse est toujours supérieure à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'excentricité d'une ellipse est toujours comprise entre 0 et 1. Elle vaut 0 pour un cercle et tend vers 1 pour une ellipse très allongée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":18814,"question":"Quelle est l'équation réduite d'une hyperbole dont les asymptotes sont y = ±(b\/a)x ?","option_a":"A. x²\/a² + y²\/b² = 1","option_b":"B. x²\/a² - y²\/b² = 1","option_c":"C. y² = 4ax","option_d":"D. (x²\/a²) - (y²\/b²) = -1","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'équation réduite d'une hyperbole avec des asymptotes y = ±(b\/a)x est x²\/a² - y²\/b² = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. x²\/a² + y²\/b² = 1\", \"b\": \"B. x²\/a² - y²\/b² = 1\", \"c\": ","_debug_options_count":4},{"id":18815,"question":"Un satellite en orbite elliptique autour de la Terre a une excentricité de 0,8. Quelle est la nature de sa trajectoire ?","option_a":"A. Cercle","option_b":"B. Ellipse","option_c":"C. Parabole","option_d":"D. Hyperbole","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une excentricité de 0,8 (0 \u003C e \u003C 1) correspond à une trajectoire elliptique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. Cercle\", \"b\": \"B. Ellipse\", \"c\": \"C. Parabole\", \"d\": \"D. Hyper","_debug_options_count":4},{"id":18816,"question":"La directrice d'une parabole est toujours parallèle à son axe de symétrie.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La directrice d'une parabole est toujours perpendiculaire à son axe de symétrie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":18817,"question":"Quelle conique a une équation de la forme Ax² + Bxy + Cy² + Dx + Ey + F = 0 avec B² - 4AC = 0 ?","option_a":"A. Ellipse","option_b":"B. Hyperbole","option_c":"C. Parabole","option_d":"D. Cercle","option_e":"","option_f":"","bonne_reponse":"c","explication":"Si B² - 4AC = 0, l'équation représente une parabole (ou une conique dégénérée).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. Ellipse\", \"b\": \"B. Hyperbole\", \"c\": \"C. Parabole\", \"d\": \"D. Ce","_debug_options_count":4},{"id":18818,"question":"Quel est l'excentricité d'une hyperbole d'équation x²\/9 - y²\/16 = 1 ?","option_a":"A. 5\/3","option_b":"B. 3\/5","option_c":"C. 16\/9","option_d":"D. 9\/16","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une hyperbole x²\/a² - y²\/b² = 1, l'excentricité est e = √(1 + b²\/a²) = √(1 + 16\/9) = 5\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. 5\/3\", \"b\": \"B. 3\/5\", \"c\": \"C. 16\/9\", \"d\": \"D. 9\/16\"}}","_debug_options_count":4}]