`y=5/12` Write the standard form of the equation of the parabola with the given directrix and vertex at (0,0)

We are asked to write the equation of the parabola with directrix y=5/12 and vertex at the origin:

The equation for a parabola with vertex at the origin and focus (0,a) is `x^2=4ay `

Since the vertex is the midpoint of the perpendicular segment from the focus to the directrix we find the focus to be at (0,-5/12).

The equation we seek is ` x^2=-5/3y `

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