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

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## Answers ( )

Answer: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

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:

Simplify that a bit:

Solving for y^2:

Answer: x = -1/8y^2Step-by-step explanationFocus: (-2,0)Directrix: x=2It meets the criteria.