Question

Find the equation of the parabola given its focus is at (2,5) and its directrix is at y=1. Can you please help me figure this out, I don't know how to solve it or anything.

Answer 1

so, notice the picture below

based on those points, the parabola is vertical and opening upwards

now, bear in mind that, the vertex is at h,k
and there's a "p" distance from the vertex, to the focus point, and the same "p" distance to the directrix, so, the vertex is really half-way between the focus point and directrix

so... all you need, is to get the "p" distance, and you'd know what h,k are
then plug all three p,h,k in the equation 4p(y - k) = (x - h)²