Quiz — Correction de la série coniques - Parabole.pdf

Question 1 sur 10 20:00

[{"id":24214,"question":"Quelle est la propriété géométrique qui définit une parabole ?","option_a":"L'ensemble des points équidistants d'un point fixe et d'une droite fixe","option_b":"L'ensemble des points équidistants de deux points fixes","option_c":"L'ensemble des points dont la somme des distances à deux points fixes est constante","option_d":"L'ensemble des points dont la différence des distances à deux points fixes est constante","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une parabole est définie comme l'ensemble des points équidistants d'un point fixe appelé foyer et d'une droite fixe appelée directrice.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"L'ensemble des points équidistants d'un point fixe et d'une droi","_debug_options_count":4},{"id":24215,"question":"L'équation y = 2x² - 4x + 1 représente une parabole.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Cette équation est de la forme y = ax² + bx + c, donc elle représente bien une parabole verticale.","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":24216,"question":"Quel est le sommet de la parabole d'équation y = (x - 3)² + 2 ?","option_a":"(3, 2)","option_b":"(2, 3)","option_c":"(0, 0)","option_d":"(1, 1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La forme canonique y = a(x - h)² + k donne directement le sommet (h, k). Ici, h = 3 et k = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"(3, 2)\", \"b\": \"(2, 3)\", \"c\": \"(0, 0)\", \"d\": \"(1, 1)\"}}","_debug_options_count":4},{"id":24217,"question":"La distance entre le sommet et le foyer d'une parabole est appelée :","option_a":"Paramètre p","option_b":"Rayon","option_c":"Focale","option_d":"Excentricité","option_e":"","option_f":"","bonne_reponse":"a","explication":"Dans une parabole, la distance entre le sommet et le foyer est notée p et est égale à la distance entre le sommet et la directrice.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Paramètre p\", \"b\": \"Rayon\", \"c\": \"Focale\", \"d\": \"Excentricité\"}","_debug_options_count":4},{"id":24218,"question":"Une parabole horizontale a toujours une équation de la forme :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une parabole horizontale s'ouvre vers la gauche ou la droite et a une équation de la forme x = ay² + by + c.","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":24219,"question":"Quel est le foyer de la parabole d'équation y² = 8x ?","option_a":"(2, 0)","option_b":"(0, 2)","option_c":"(8, 0)","option_d":"(0, 8)","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation y² = 4px donne un foyer en (p, 0). Ici, 4p = 8 donc p = 2, d'où le foyer (2, 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\": \"(2, 0)\", \"b\": \"(0, 2)\", \"c\": \"(8, 0)\", \"d\": \"(0, 8)\"}}","_debug_options_count":4},{"id":24220,"question":"La directrice d'une parabole est toujours parallèle à l'axe des abscisses.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La directrice est toujours perpendiculaire à l'axe de symétrie de la parabole. Pour une parabole verticale, elle est horizontale, mais pour une parabole horizontale, elle est verticale.","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":24221,"question":"Quelle est l'équation de la parabole de sommet (1, -2) et de foyer (1, 0) ?","option_a":"y = 2(x - 1)² - 2","option_b":"y = (1\/8)(x - 1)² - 2","option_c":"x = 2(y + 2)² - 1","option_d":"y = 8(x - 1)² - 2","option_e":"","option_f":"","bonne_reponse":"b","explication":"La distance entre le sommet (1, -2) et le foyer (1, 0) est p = 2. L'équation est y = (1\/(4p))(x - h)² + k = (1\/8)(x - 1)² - 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"y = 2(x - 1)² - 2\", \"b\": \"y = (1\/8)(x - 1)² - 2\", \"c\": \"x = 2(y","_debug_options_count":4},{"id":24222,"question":"Pour une parabole d'équation y = ax² + bx + c, le sommet a pour abscisse :","option_a":"-b\/(2a)","option_b":"b\/(2a)","option_c":"-a\/(2b)","option_d":"c\/(2a)","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'abscisse du sommet d'une parabole y = ax² + bx + c est donnée par x = -b\/(2a).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"-b\/(2a)\", \"b\": \"b\/(2a)\", \"c\": \"-a\/(2b)\", \"d\": \"c\/(2a)\"}}","_debug_options_count":4},{"id":24223,"question":"La parabole d'équation x² = -12y s'ouvre vers :","option_a":"Le haut","option_b":"Le bas","option_c":"La droite","option_d":"La gauche","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'équation x² = -4py représente une parabole qui s'ouvre vers le bas. Ici, -4p = -12 donc p = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Le haut\", \"b\": \"Le bas\", \"c\": \"La droite\", \"d\": \"La gauche\"}}","_debug_options_count":4}]