Question

Derive the equation of the parabola with a focus at (2, −1) and a directrix of y = −one half. help?

Answer 1

"The parabola is the locus of points in that plane that are equidistant from both the directrix and the focus." (wikipedia)

Let (x,y) be a point on the required parabola. According to the definition the distance between (x,y) and the directrix must equal the distance between the point and the the focus. So, write the expressions for these two distances, equate them and you have your equation for the required parabola.

Enough to go on?