`x=-1/18` 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 x=-1/18 and vertex at the origin:

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

Since the vertex is the midpoint of the perpendicular segment from the focus to the directrix we find the focus at (1/18,0).

Thus the equation we seek is `y^2=2/9x `

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