ind an equation for the parabola that has its vertex at the origin and satisfies the given condition. focus F = (0,-1/2)?

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  • Lopez
    Lv 5
    4 years ago
    Best Answer

    F = (0,-1/2) , vertex at the origin , so

    the Directrix is : y = 1/2

    Let L be y = 1/2

    Suppose P(x,y) is a point on the parabola, then

    d(P,L) = PF

    1/2 - y = √ [ x^2 + ( y + 1/2 )^2 ]

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

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

    2y = - x^2

    y = - (1/2)x^2 ... Ans

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