precalculus

Find the focus, directrix, and focal diameter of the parabola.
y2 = 8x

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  1. This is an X-parabola.

    Y^2 = 8x.
    X = (1/8)y^2

    k = Yv = -b/2a = 0/(1/4) = 0
    h = Xv = (1/8*0^2 = 0.
    V(h,k) = V(0,0).

    D(X1,K), V(h,k), F(X2,K).
    D(X1,0), V(0,0), F(X2,0).

    DV = 0-X1 = 1/4a.
    0-X1 = 1/(1/2) = 2.
    X1 = -2.

    VF = X2-0 = 1/4a
    X2 = 1/(1/2) = 2

    Focal Dia.(Ver. line).
    A(2,Y1), F(2,0), B(2,Y2).

    a = 1/8
    1/a = 8 = Focal Dia.

    AF = 0-Y1 = 8/2 = 4.
    Y1 = -4.

    FB = Y2-0 = 8/2 = 4
    Y2 = 4.

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