Find the standard form of the equation of the parabola with a focus at (0, 4) and a directrix at y = -4. Answer choices: y = 1/16x2 y2 = 16x y2 = 4x y = 1/4x2

a) The standard form of the equation

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Explanation:-

    A parabola is the set of all points in a plane that are equidistant from a fixed line and a fixed point (not in a line) in the plane

•The Fixed line is called the directrix of the parabola.

•The Fixed point is called the focus of the parabola.

•A line through the focus and perpendicular to the directrix is called the axis of the parabola.

•The point of intersection of parabola with the axis is called the vertex of the parabola.

Given Focus of the parabola S(0,a)= (0,4)

Given Focus is lies on y-axis and the directrix is parallel to x-axis

Given directrix of the parabola y = -4

Directrix     y = -a

Standard form of the parabola

                                x² = 4ay

                               x² = 4(4)y

                              x² = 16y

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