text: find an equation of the parabola that has a focus at (9,7) and a vertex at (9,2)? y= (x-9)^2+2  is not the right answer you've got to find the directrix line first. then a point on the parabola is one that is equidistant from the focus and the directrix. the directrix is always perpendicular to the line passing through the focus and the vertex, and it lies at the same distance from the vertex as the focus does. so, in this case, the directrix is the line y = -3 (draw a diagram). the square of the dist of a point (x, y) from this line is just (y+3)^2. so the equal-dist condition for (x, y) to be on the parabola is   (x-9)^2 + (y-7)^2 = (y+3)^2  which expands to   y = (1/20)(x-9)^2 + 2.