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.

helperid1839321
Feb 1, 2018