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What is the equation of the directrix of the parabola defined by the equation of x^2=24y

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Explanation:

The equation of a parabola with vertex at the origin and axis of symmetry along the y-axis is given by x^2 = 4py, where p is the distance from the vertex to the focus and from the vertex to the directrix.

Comparing this to the given equation x^2 = 24y, we see that 4p = 24, so p = 6. Therefore, the distance from the vertex to the directrix is also 6.

Since the parabola is symmetric about the y-axis, the directrix is a horizontal line located at a distance of 6 units below the vertex. Thus, the equation of the directrix is y = -6.

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