[{"data":1,"prerenderedAt":128},["ShallowReactive",2],{"\u002Fpublic\u002Ftopics\u002Fgeometria\u002Fgeometria-analitica?{}":3,"topics-with-content:geometria":113},{"course":4,"topic":12,"counts":17,"universities":22,"channels":34,"sampleQuestions":69,"sameName":112},{"id":5,"slug":6,"name":7,"shortName":8,"area":9,"icon":10,"sortOrder":11},3,"geometria","Geometría","Geom.","math","i-lucide-triangle",2,{"id":13,"courseId":5,"slug":14,"name":15,"sortOrder":16},313,"geometria-analitica","Geometría analítica",12,{"topicId":13,"courseId":5,"questions":18,"classes":19,"videos":20,"minutes":21},29,242,179,4903,[23,32],{"universityId":24,"questions":25,"years":26},1,17,[27,28,29,30,31],2026,2025,2024,2023,2022,{"universityId":11,"questions":16,"years":33},[27,28,29,30,31],[35,38,41,44,47,49,52,54,57,60,62,65,67],{"name":36,"classes":37},"Alberto Cruz",58,{"name":39,"classes":40},"Academia Internet",41,{"name":42,"classes":43},"Academia Grupo Ciencias",37,{"name":45,"classes":46},"Academia ipluton",32,{"name":48,"classes":25},"Academias Aduni y César Vallejo",{"name":50,"classes":51},"Salón Sapiens",14,{"name":53,"classes":16},"Ciclo Uni-San Marcos",{"name":55,"classes":56},"CEPRE UNMSM",10,{"name":58,"classes":59},"META VILLARREAL",5,{"name":61,"classes":59},"Trilce Multimedia",{"name":63,"classes":64},"Pamer Corporación Educativa",4,{"name":66,"classes":64},"Saco Oliveros",{"name":68,"classes":5},"Academia_Pitagoras",[70,95],{"id":71,"courseId":5,"topicId":13,"pastExamId":72,"stem":73,"options":74,"correctKey":82,"explanation":90,"difficulty":64,"status":91,"source":92,"stats":93},1664,198,"Dada la hipérbola de ecuación\n$\\dfrac{(y-7)^{2}}{3^{2}}-\\dfrac{(x-4)^{2}}{4^{2}}=1.$\nDetermine la ecuación de la circunferencia que pasa por los focos de la hipérbola y por un extremo de su eje conjugado.",[75,78,81,84,87],{"key":76,"text":77},"A","$x^{2}+y^{2}-\\dfrac{23}{4}x-14y+30=0$",{"key":79,"text":80},"B","$x^{2}+y^{2}-\\dfrac{23}{4}x+14y-31=0$",{"key":82,"text":83},"C","$x^{2}+y^{2}-\\dfrac{23}{4}x-14y+31=0$",{"key":85,"text":86},"D","$x^{2}+y^{2}+\\dfrac{23}{4}x+14y+31=0$",{"key":88,"text":89},"E","$x^{2}+y^{2}+\\dfrac{23}{4}x-14y+31=0$","","published","UNI 2026-1 · Matemática",{"attempts":94,"accuracy":94},0,{"id":96,"courseId":5,"topicId":13,"pastExamId":97,"stem":98,"options":99,"correctKey":76,"explanation":90,"difficulty":5,"status":91,"source":110,"stats":111},1300,192,"Determine la ecuación en coordenadas transformadas $X'Y'$ de una recta cuya ecuación en coordenadas originales es $\\mathscr{L}\\colon y=x+3\\sqrt{2}$, luego de que los ejes $XY$ han sido rotados 45° en sentido antihorario.",[100,102,104,106,108],{"key":76,"text":101},"$y'=3$",{"key":79,"text":103},"$y'=-3$",{"key":82,"text":105},"$y'=\\sqrt{2}$",{"key":85,"text":107},"$y'=-\\sqrt{2}$",{"key":88,"text":109},"$y'=\\dfrac{\\sqrt{2}}{3}$","UNI 2025-1 · Matemática",{"attempts":94,"accuracy":94},[],[114,115,116,117,118,119,120,121,122,123,124,125,13,126,127],301,302,303,304,305,306,307,308,309,310,311,312,314,315,1791501527176]