Question

What is the equation of the quadratic graph with a focus of (5,6) and a directrix of y=2

Answer 1

Check the picture below, notice the distance from the focus to the directrix

bear in mind that, the vertex is a distance "p" from the focus point and a distance "p" from the directrix, that simply means, the vertex is half-way between both of those fellows

in this case, the focus point is above the directrix, that means, the parabola is vertical and opens upwards, "p" is  a positive number for the focus/point form

$\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} (x-{{ h}})^2=4{{ p}}(y-{{ k}}) \\ \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}$

so.. check the graph, you know what h,k are, and p, so, plug them in