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algebra 2

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Directions: The focus and directrix of a parabola are given. Write an equation for each parabola.

(2,4) y = 6

May you explain the procedures on how to solve this equation? Please be detailed on each step.

  • algebra 2 -

    I assume you have to use the basic definition of a parabola as the set of points equidistant from the focal point (2,4) and the line y=6

    Make a sketch and let P(x,y) be any point on the parabola

    so √((x-2)^2 + (y-4)^2) = √(y-6)^2

    square both sides
    (x-2)^2 + (y-4)^2 = (y-6)^2

    x^2 - 4x + 4 + y^2 - 8y + 16 = y^2 - 12y + 36

    y = -(1/4)x^2 + x + 4

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