Quiz — serie coniques 3.pdf

Question 1 sur 10 20:00

[{"id":31690,"question":"Quelle équation représente une ellipse centrée à l’origine ?","option_a":"x² + y² = 1","option_b":"x²\/a² + y²\/b² = 1","option_c":"x²\/a² - y²\/b² = 1","option_d":"y = ax² + bx + c","option_e":"","option_f":"","bonne_reponse":"b","explication":"L’équation x²\/a² + y²\/b² = 1 représente une ellipse centrée à l’origine avec a et b les demi-axes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"x² + y² = 1\", \"b\": \"x²\/a² + y²\/b² = 1\", \"c\": \"x²\/a² - y²","_debug_options_count":4},{"id":31691,"question":"Une parabole a toujours deux foyers.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une parabole n’a qu’un seul foyer et une seule directrice, contrairement à l’ellipse et l’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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":31692,"question":"Quelle est l’équation d’une hyperbole dont les asymptotes sont y = ±(b\/a)x ?","option_a":"x²\/a² + y²\/b² = 1","option_b":"x²\/a² - y²\/b² = 1","option_c":"y² = 4px","option_d":"(x-h)²\/a² - (y-k)²\/b² = 1","option_e":"","option_f":"","bonne_reponse":"b","explication":"L’équation x²\/a² - y²\/b² = 1 représente une hyperbole avec des asymptotes y = ±(b\/a)x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"x²\/a² + y²\/b² = 1\", \"b\": \"x²\/a² - y²\/b² = 1\", \"c\": \"y² =","_debug_options_count":4},{"id":31693,"question":"La directrice d’une parabole est toujours perpendiculaire 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 parallèle à son axe de symétrie, pas perpendiculaire.","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":31694,"question":"Quel est le foyer d’une parabole d’équation y² = 4px ?","option_a":"(p, 0)","option_b":"(0, p)","option_c":"(0, -p)","option_d":"(-p, 0)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour y² = 4px, le foyer est situé en (p, 0).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"(p, 0)\", \"b\": \"(0, p)\", \"c\": \"(0, -p)\", \"d\": \"(-p, 0)\"}}","_debug_options_count":4},{"id":31695,"question":"Les asymptotes d’une hyperbole sont toujours des droites sécantes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Les asymptotes d’une hyperbole sont parallèles entre elles (pour une hyperbole standard) ou sécantes pour une hyperbole tournée.","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":31696,"question":"Quelle conique a une excentricité e = 1 ?","option_a":"Ellipse","option_b":"Parabole","option_c":"Hyperbole","option_d":"Cercle","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une parabole a une excentricité e = 1, tandis que l’ellipse a e \u003C 1 et l’hyperbole e \u003E 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\": \"Ellipse\", \"b\": \"Parabole\", \"c\": \"Hyperbole\", \"d\": \"Cercle\"}}","_debug_options_count":4},{"id":31697,"question":"L’équation x² - y² = 1 représente :","option_a":"Une ellipse","option_b":"Une parabole","option_c":"Une hyperbole","option_d":"Un cercle","option_e":"","option_f":"","bonne_reponse":"c","explication":"x² - y² = 1 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\": \"c\", \"options\": {\"a\": \"Une ellipse\", \"b\": \"Une parabole\", \"c\": \"Une hyperbole\", \"d\": \"Un","_debug_options_count":4},{"id":31698,"question":"Le cercle est un cas particulier de l’ellipse.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un cercle est un cas particulier d’ellipse où les deux demi-axes sont égaux (a = b).","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":31699,"question":"Quelle est la relation entre les paramètres a, b et c pour une ellipse ?","option_a":"c² = a² + b²","option_b":"c² = a² - b²","option_c":"b² = a² + c²","option_d":"a² = b² + c²","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour une ellipse, la relation est c² = a² - b², où c est la distance du centre à un foyer.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"c² = a² + b²\", \"b\": \"c² = a² - b²\", \"c\": \"b² = a² + c²\",","_debug_options_count":4}]