Find the standard form of the equation of the parabola with a focus at (-2, 0) and a directrix at x = 2. answers:

Question

Find the standard form of the equation of the parabola with a focus at (-2, 0) and a directrix at x = 2.

answers:

a) y2 = 4x

b)8y = x2

c)x = 1 divided by 8y2

d) y = 1 divided by 8×2

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2 weeks 2021-10-10T20:56:50+00:00 2 Answers 0

Answers ( )

    0
    2021-10-10T20:58:08+00:00

    Answer:

    y^2=\frac{1}{8}x

    Step-by-step explanation:

    The focus lies on the x axis and the directrix is a vertical line through x = 2.  The parabola, by nature, wraps around the focus, or “forms” its shape about the focus.  That means that this is a “sideways” parabola, a “y^2” type instead of an “x^2” type.  The standard form for this type is

    (x-h)=4p(y-k)^2

    where h and k are the coordinates of the vertex and p is the distance from the vertex to either the focus or the directrix (that distance is the same; we only need to find one).  That means that the vertex has to be equidistant from the focus and the directrix.  If the focus is at x = -2 y = 0 and the directrix is at x = 2, midway between them is the origin (0, 0).  So h = 0 and k = 0.  p is the number of units from the vertex to the focus (or directrix).  That means that p=2.  We fill in our equation now with the info we have:

    (x-0)=4(2)(y-0)^2

    Simplify that a bit:

    x=8y^2

    Solving for y^2:

    y^2=\frac{1}{8}x

  1. Emma
    0
    2021-10-10T20:58:19+00:00

    Answer: x = -1/8y^2

    Step-by-step explanation

    Focus: (-2,0)

    Directrix: x=2

    It meets the criteria.

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