precalculus

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Find the focus, directrix, and focal diameter of the parabola.
x2 = 5y

focus (x, y) = 0, 5/4
directrix:y=-5/4 focal diameter=5
Sketch its graph?
my answers seem to be correct but i cannnot sketch the graph correctly.

  • precalculus -

    X^2 = 5y. Y-parabola.
    Y = (1/5)x^2
    a = 1/5, 4a = 4/5, 1/4a = 5/4.

    h = Xv = -b/2a = 0/(2/5) = 0.
    k = Yv = (1/5)*0^2 = 0.
    V(h,k) = V(0,0).

    D(h,Y1), V(h,k), F(h,Y2). Ver. Line.
    D(0,Y1), V(0,0), F(0,Y2).

    DV = 0-Y1 = 1/4a
    0-Y1 = 1/4a = 5/4.
    Y1 = -5/4.

    VF = Y2-0 = 1/4a.
    Y2-0 = 1/4a = 5/4
    Y2 = 5/4.

    Focal Dia. = 1/a = 1/(1/5) = 5.
    A(X1,5/4), F(0,5/4), B(X2,5/4). Hor line

    AF = 0-X1 = 5/2
    0-X1 = 5/2
    X1 = -5/2.

    FB = X2-0 = 5/2
    X2 = 5/2.

    Your answers are correct!

    To graph the parabola, select values of
    X below and above h(Xv); and calculate
    the corresponding value of Y in each
    case.

    (x,Y). Y = (1/5)x^2.
    (-3,9/5).
    (-2,4/5).
    (-1,1/5).
    V(0,0).
    (1,1/5).
    (2,4/5).
    (3,9/5).

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