[{"question":"Hyperbola m\u00e1 ohnisk\u00e1 [-10, 2] a [16, 2]. D\u013a\u017eka hlavnej osi je 24. Ak\u00e1 je rovnica hyperboly?","answers":["25x2<\/sup> - 144y2<\/sup> - 150x + 576y - 3951 = 0","25x2<\/sup> - 144y2<\/sup> - 576y - 3951 = 0","25x2<\/sup> - 144y2<\/sup> - 150x + 576y - 51 = 0","25x2<\/sup> - 144y2<\/sup> - 150x + 56y - 3951 = 0"],"correct":"25x2<\/sup> - 144y2<\/sup> - 150x + 576y - 3951 = 0","order":"1"},{"question":"Ak\u00e1 je osov\u00e1 rovnica hyperboly, ktor\u00e1 prech\u00e1dza bodmi [9\/2, -1] a [6, 8]?","answers":["4x2<\/sup> + y2<\/sup> = 80","4x2<\/sup> - 3y2<\/sup> = 80","4x2<\/sup> - y2<\/sup> = 80","4x2<\/sup> - y2<\/sup> = 8"],"correct":"4x2<\/sup> - y2<\/sup> = 80","order":"2"},{"question":"N\u00e1jdite doty\u010dnicu hyperboly s rovnicou 16x2<\/sup> - 9y2<\/sup> + 32x + 18y - 137 = 0, pri\u010dom t\u00e1to doty\u010dnica je kolm\u00e1 na priamku x + 4y - 3 = 0.","answers":["4x - y \u00b1 8*\u221a2 = 0","4x - y + 5 \u00b1 8 = 0","4x - y + 5 \u00b1 \u221a2 = 0","4x - y + 5 \u00b1 8*\u221a2 = 0"],"correct":"4x - y + 5 \u00b1 8*\u221a2 = 0","order":"3"},{"question":"N\u00e1jdite osov\u00fa rovnicu hyperboly, ktor\u00e1 sa v bode [5, 9\/4] dot\u00fdka priamky 5x - 4y - 16 = 0","answers":["9x2<\/sup> - 16y2<\/sup> = 14","9x2<\/sup> - 16y2<\/sup> = 144","9x2<\/sup> + 16y2<\/sup> = 14","9x2<\/sup> + 16y2<\/sup> = 144"],"correct":"9x2<\/sup> - 16y2<\/sup> = 144","order":"4"},{"question":"Ak\u00fd uhol zvieraj\u00fa krivky x2<\/sup>\/25 + y2<\/sup>\/9 = 1 a x2<\/sup>\/4 - y2<\/sup>\/12 = 1?","answers":["30","60","90","120"],"correct":"90","order":"5"},{"question":"Ak\u00e1 je rovnica hyperboly, ktor\u00e1 m\u00e1 asymptoty 2y = \u00b1 x a dot\u00fdka sa priamky 5x - 6y - 8 = 0?","answers":["x2<\/sup> - 4y2<\/sup> = 16","x2<\/sup> - 4y2<\/sup> = 6","x2<\/sup> - y2<\/sup> = 16","4x2<\/sup> - 4y2<\/sup> = 16"],"correct":"x2<\/sup> - 4y2<\/sup> = 16","order":"6"},{"question":"Ur\u010dte stred hyperboly s rovnicou 4x2<\/sup> - 9y2<\/sup> + 16x - 18y - 29 = 0","answers":["2.1","(2, -1)","(2, 2)","(-2, -1)"],"correct":"(-2, -1)","order":"7"},{"question":"Ur\u010dte vrcholy hyperboly z predch\u00e1dzaj\u00faceho pr\u00edkladu:","answers":["[-5, -1] a [1, -1]","[5, -1] a [1, -1]","[-5, -1] a [-1, -1]","[-5, -1] a [1, 1]"],"correct":"[-5, -1] a [1, -1]","order":"8"},{"question":"Urt\u010de ohnisk\u00e1 hyperboly z predch\u00e1dzaj\u00faceho pr\u00edkladu:","answers":["[-2\u00b1\u221a14, -1]","[-2\u00b1\u221a13, -1]","[-1\u00b1\u221a13, -1]","[-2\u00b1\u221a13, 1]"],"correct":"[-2\u00b1\u221a13, -1]","order":"9"},{"question":"Ur\u010dte asymptoty hyperboly z predch\u00e1dzaj\u00faceho pr\u00edkladu:","answers":["2x - 3y - 1 = 0 a 2x + 3y + 7 = 0","2x + 3y + 1 = 0 a os y","2x - 3y + 1 = 0 a os x","2x - 3y + 1 = 0 a 2x + 3y + 7 = 0"],"correct":"2x - 3y + 1 = 0 a 2x + 3y + 7 = 0","order":"10"}]