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# Formula for parabola given focus and directrix

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I was in math class the other day. We are currently covering the equation of a parabola given a directrix. I think I might have found an equation in vertex form ($$f(x)=a(x-h)^2+k$$, where h = x-value f vertex and k = y-value of vertex) given the coordinates of the focus as $$(b,\ d)$$ and the directrix as $$y=c$$.

$$\begin{matrix}a=\frac{\frac{1}{d-c}}{2}\\h=d\\k=\frac{c+d}{2}\end{matrix}$$

Is this correct? Because I tried it in 2 different scenarios, and it worked both times.

Feb 1, 2018