<prompt> Fumana equation ea parabola e fanoeng tsepamiso le directrixTsepamiso ea maikutlo: 2, 4, Directrix: y 0  <response>: Instruction in English: Find the equation of the parabola given the focus and directrix . Response in English: A parabola is defined as the set of all points equidistant from a point called the focus and a line called the directrix.Let x, y be a point on the parabola with focus 2,4 and directrix y0. By definition of the parabola, the distance from x, y to the focus is equal to the distance from x,y to the directrix.Using the distance formula, we can say that:sqrtx-22 y-42 y-0Squaring both sides:x-22 y-42 y2x2 - 4x 4 y-42 y2x2 - 4x 4 y2 - 8y 16 y2x2 - 4x 16 - 8y 16 0Which simplifies to:x2 - 4x - 8y 36 0.After completing the square in the x to put the equation in standard form, we have:x - 22 - 4 - 8y 36 0.Simplifying, we getx - 22 8y - 32Finally, the standard form of the equation of the parabola with focus 2, 4 and directrix y 0 isx - 22 8y - 4. . Response in Sesotho: Parabola e hlalosoa e le sehlopha sa lintlha tsohle tse lekanang ho tloha sebakeng se bitsoang focus le mola o bitsoang directrix. E re x, y e be ntlha ya papiso e tsepamisitseng maikutlo 2,4 le directrix y0. Ho ea ka tlhaloso ea papiso, sebaka ho tloha ho x, y ho ea ho tsepamiso e lekana le sebaka sa ho tloha x,y ho ea ho directrix. Ka ho sebelisa mokhoa oa sebaka, re ka re: sqrtx-22 y-42 y-0 Squaring mahlakore ka bobeli: x-22 y-4 2 y2 x2 - 4x 4 y-42 y2 x2 - 4x 4 y2 - 8y 16 y2 x2 - 4x 16 - 8y 16 0 E nolofatsang ho: x2 - 4x - 8y 36 0. Ka mora ho tlatsa sekoere ho x ho beha equation ka mokhoa o tloaelehileng, re na le: x - 22 - 4 - 8y 36 0. Ho nolofatsa, re fumana x - 22 8y - 32 Qetellong, mokhoa o tloaelehileng oa tekano ea parabola ka ho tsepamisa maikutlo 2, 4 le directrix y 0 ke x - 2 2 8y - 4. 