[{"question":"N\u00e1jdite osov\u00fa rovnicu elipsy, ktor\u00e1 prech\u00e1dza bodmi [2, 3] a [-1, -4]","answers":["x2<\/sup> + 4y2<\/sup> = 88","x2<\/sup> + 4y2<\/sup> = 100","7x2<\/sup> + 3y2<\/sup> = 55","x2<\/sup> + 4y2<\/sup> = 36"],"correct":"7x2<\/sup> + 3y2<\/sup> = 55","order":"1"},{"question":"N\u00e1jdite osov\u00fa rovnicu elipsy, ktor\u00e1 prech\u00e1dza bodmi [-6, -4] a [5, 5*\u221a3\/2]","answers":["x2<\/sup> + 3y2<\/sup> = 55","x2<\/sup> + 4y2<\/sup> = 36","7x2<\/sup> + 3y2<\/sup> = 55","x2<\/sup> + 4y2<\/sup>"],"correct":"x2<\/sup> + 4y2<\/sup>","order":"2"},{"question":"N\u00e1jdite osov\u00fa rovnicu elipsy, ktor\u00e1 prech\u00e1dza bodmi [3, -3*\u221a3\/2] a [-4, \u221a5]","answers":["x2<\/sup> + y2<\/sup> = 25","x2<\/sup> + 4y2<\/sup> = 36","x2<\/sup> + 4y2<\/sup> = 100","7x2<\/sup> + 3y2<\/sup> = 55"],"correct":"x2<\/sup> + 4y2<\/sup> = 36","order":"3"},{"question":"N\u00e1jdite s\u00faradnice stredu a ur\u010dte d\u013a\u017eku polos\u00ed elipsy, ktor\u00e1 je vyjadren\u00e1 rovnicou 16x2<\/sup> + 25y2<\/sup> - 64x -150y - 111 = 0","answers":["S = [1,2], a = 3, b = 2","S = [2, 3], a = 5, b = 4","S = [-2, 1], a = 4, b = 1","S = [-2, 1], a = 4, b = 3"],"correct":"S = [2, 3], a = 5, b = 4","order":"4"},{"question":"N\u00e1jdite s\u00faradnice stredu a ur\u010dte d\u013a\u017eku polos\u00ed elipsy, ktor\u00e1 je vyjadren\u00e1 rovnicou 4x2<\/sup> + 9y2<\/sup> - 8x -36y + 4 = 0","answers":["S = [1, 2], a = 3, b = 2","S = [-2, 1], a = 4, b = 3","S = [2, 3], a = 5, b = 4","S = [3, 3], a = 5, b = 4"],"correct":"S = [1, 2], a = 3, b = 2","order":"5"},{"question":"N\u00e1jdite s\u00faradnice stredu a ur\u010dte d\u013a\u017eku polos\u00ed elipsy, ktor\u00e1 je vyjadren\u00e1 rovnicou 9x2<\/sup> + 16y2<\/sup> + 36x - 32y - 92 = 0","answers":["S = [-2, 1], a = 4, b = 3","S = [-2, 4], a = 4, b = 3","S = [1, 2], a = 3, b = 2","S = [2, 3], a = 5, b = 4"],"correct":"S = [-2, 1], a = 4, b = 3","order":"6"},{"question":"Do elipsy, ktor\u00e1 m\u00e1 hlavn\u00fa d\u013a\u017eku poloos\u00ed a, b je vp\u00edsan\u00fd \u0161tvorec so stranou s. \u010comu sa rovn\u00e1 d\u013a\u017eka tejto strany?","answers":["s = ab\/\u221a(a2<\/sup> + b2<\/sup>)","s = 2\/\u221a(a2<\/sup> + b2<\/sup>)","s = 2ab","s = 2ab\/\u221a(a2<\/sup> + b2<\/sup>)"],"correct":"s = 2ab\/\u221a(a2<\/sup> + b2<\/sup>)","order":"7"},{"question":"Bodom [6, 10] s\u00fa veden\u00e9 doty\u010dnice elipsy, ktor\u00e1 je vyjadren\u00e1 rovnicou x2<\/sup>\/36 + y2<\/sup>\/25 = 1. Ak\u00fd uhol s \u0148ou zvieraj\u00fa?","answers":["56\u00b0","57\u00b0","58\u00b0","59\u00b0"],"correct":"58\u00b0","order":"8"},{"question":"M\u00e1me dan\u00fa excentricitu elipsy (e = 2) a doty\u010dnicu k elipse s rovnicou 2x + 3y + 9 = 0. N\u00e1jdite osov\u00fa rovnicu elipsy.","answers":["5x2<\/sup> + 9y2<\/sup> = 45","5x2<\/sup> - 9y2<\/sup> = 45","5x2<\/sup> + 9y2<\/sup> = -45","5x2<\/sup> + 9x= 45"],"correct":"5x2<\/sup> + 9y2<\/sup> = 45","order":"9"},{"question":"Ak\u00e1 je osov\u00e1 rovnica elipsy, ktor\u00e1 sa v bode [5, -3] dot\u00fdka priamky 3x - 4y - 27 = 0?","answers":["9x2<\/sup> - 20x = 405","9x2<\/sup> + 20x = -405","9x2<\/sup> + 20x = 45","9x2<\/sup> + 20x = 405"],"correct":"9x2<\/sup> + 20x = 405","order":"10"}]