Focus at (0- -5)- directrix y - 5SolutionLet ( x0 - y0 ) be any point.docx

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Focus at (0, -5), directrix y = 5 Solution Let ( x 0 , y 0 ) be any point on the parabola. Find the distance between ( x 0 , y 0 ) and the focus. Then find the distance between ( x 0 , y 0 ) and directrix. Equate these two distance equations and the simplified equation in x 0 and y 0 is equation of the parabola. The distance between ( x 0 , y 0 ) and (0, -5) is [(x 2 )+(y+5) 2 ] The distance between ( x 0 , y 0 ) and the directrix, y = 5 is | y 0 â€“ 5|. Equate the two distance expressions and square on both sides. (x 0 2 )+(y 0 +5) 2 = ( y 0 â€“ 5) 2 Simplify and bring all terms to one side: Write the equation with y 0 on one side: x 2 = -20y This equation in ( x 0 , y 0 ) is true for all other values on the parabola and hence we can rewrite with ( x , y ). So, the equation of the parabola with focus (0, -5) and directrix is y = 5 is x 2 = -20y .

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