The parabola with equation y = 18x − x2 passes through the origin and its focus lies at (9, f ). (a) Explain why the vertex of this parabola lies at (9, 81). 1 (b) Given that the focus is at (9,f), find the equation of the directrix. Your equation will involve f. 2 (c) Using the fact that the origin lies on this parabola, together with the expressions for the focus and directrix, find the value of f.

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