Maîtrisez les coniques : cercle, ellipse, parabole et hyperbole

Question 1 sur 10 10:00

[{"id":22728,"question":"Quelle est l'équation réduite d'un cercle de centre (0,0) et de rayon 3 ?","option_a":"x² + y² = 3","option_b":"x² + y² = 9","option_c":"x² - y² = 9","option_d":"x² + y² = 6","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'équation réduite d'un cercle de centre (0,0) et de rayon r est x² + y² = r². Ici, r = 3, donc r² = 9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22729,"question":"Une ellipse a toujours deux foyers.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une ellipse a effectivement deux foyers, situés sur son grand axe.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22730,"question":"Quelle est l'excentricité d'une parabole ?","option_a":"0","option_b":"1","option_c":"0,5","option_d":"2","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'excentricité d'une parabole est toujours égale à 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22731,"question":"L'hyperbole a-t-elle des asymptotes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une hyperbole possède deux asymptotes qui se croisent en son centre.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22732,"question":"Quelle conique a une équation de la forme y = ax² + bx + c ?","option_a":"Cercle","option_b":"Ellipse","option_c":"Parabole","option_d":"Hyperbole","option_e":"","option_f":"","bonne_reponse":"C","explication":"Cette équation représente une parabole, courbe symétrique par rapport à un axe vertical.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22733,"question":"Le cercle est un cas particulier d'ellipse.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un cercle est une ellipse dont les deux foyers coïncident au centre.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22734,"question":"Quelle est la somme des distances d'un point de l'ellipse à ses deux foyers ?","option_a":"Inférieure au grand axe","option_b":"Égale au grand axe","option_c":"Supérieure au grand axe","option_d":"Variable","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour tout point d'une ellipse, la somme des distances aux deux foyers est constante et égale à la longueur du grand axe.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22735,"question":"Une hyperbole peut-elle avoir une asymptote verticale ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une hyperbole peut avoir des asymptotes verticales et horizontales selon son orientation.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22736,"question":"Quelle conique a une excentricité strictement inférieure à 1 ?","option_a":"Cercle","option_b":"Ellipse","option_c":"Parabole","option_d":"Hyperbole","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'excentricité d'une ellipse est comprise entre 0 et 1 (exclu). Pour un cercle, elle vaut 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22737,"question":"L'équation x²\/a² - y²\/b² = 1 représente :","option_a":"Un cercle","option_b":"Une ellipse","option_c":"Une parabole","option_d":"Une hyperbole","option_e":"","option_f":"","bonne_reponse":"D","explication":"Cette équation est celle d'une hyperbole centrée à l'origine, avec des asymptotes y = ±(b\/a)x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]