<prompt> Hlalosa hyperbola e fetang lintlheng tse fanoeng.Lintlha: 3,4, 2,-6  <response>: Instruction in English: Identify the hyperbola that passes through the given points. . Response in English: A hyperbolas standard form is given by x-h2a2 - y-k2b21 for horizontal hyperbolas or y-k2a2 - x-h2b21 for vertical hyperbolas. Where h and k are the coordinates of the center, while a and b are constant values associated with the lengths of the axes of the hyperbola. So to identify the hyperbola that passes through both 3,4 and 2,-6, we will plug the points into the general equation of a hyperbola then solve for its variables. Assuming a hyperbola in the form x-h2a2 - y-k2b21 is what we are looking for, we plug 3,4 and 2,-6 into the equation to get the following system of equations:3-h2a2 - 4-k2b212-h2a2 - -6-k2b21Simplifying the system of equations we get:3-h2a2 - 4-k2b22-h2a2 - -6-k2b23-h2 - 4-k2 2-h2 - -6-k29 - 6h h2 - 16 8k - k2 4 - 4h h2 - 36 - 12k - k2h2 - 6h - k2 8k - 7 h2 - 4h - k2 -12k - 32h -5k - 25This seems to suggest that we dont have enough information to find a unique solution. Since we only have two points from a non-degenerate conic, there are infinitely many hyperbolas that pass through both points. . Response in Sesotho: Sebopeho se tloaelehileng sa hyperbola se fanoe ke xh2a2 - yk2b21 bakeng sa hyperbolas tse rapameng kapa yk2a2 - xh2 b21 bakeng sa hyperbolas tse otlolohileng. Moo h le k e leng likhokahano tsa setsi, ha a le b e le boleng bo sa fetoheng bo amanang le bolelele ba lilepe tsa hyperbola. Kahoo ho tseba hyperbola e fetang 3,4 le 2,-6, re tla kenya lintlha ho equation e akaretsang ea hyperbola ebe re e rarolla bakeng sa mefuta-futa ea eona. Ha re nka hyperbola ka sebopeho sa xh2a2 - yk2b21 ke seo re se batlang, re hokela 3,4 le 2, -6 ho equation ho fumana mokhoa o latelang oa lipalo: 3-h2a2 - 4-k2b21 2-h2 a2 - -6-k2b21 Ho nolofatsa tsamaiso ea lipalo re fumana: 3-h2a2 - 4-k 2b22-h2a2 - -6-k2b2 3-h2 - 4-k2 2- h2 - -6-k2 9 - 6h h2 - 16 8k - k2 4 - 4h h2 - 36 - 12k - k2 h2 - 6h - k2 8k - 7 h2 - 4h - k2 -12k - 32 h -5k - 25 Sena se bonahala se fana ka maikutlo a hore ha re na boitsebiso bo lekaneng ho fumana tharollo e ikhethang. Kaha re na le lintlha tse peli feela ho tloha ho conic e sa senyehang, ho na le li-hyperbola tse ngata tse sa feleng tse fetang lintlheng tseo ka bobeli. 