What is the equation of a parabola with focus point (2,-1) and directrix y=-4

Question

i need help and work shown for this problem

Answer 1

It helps to draw this situation (graph).

The distance from F(2,-1) to directrix y=-4 is 3 units; halfway down from F is the Vertex--thus V(2,-2.5) and  p=1.5; it's the distance between V & F and also between V & directrix.

 

In general, with Vertex(h,k), equation is

4p(y-k) = (x-h)² and in this specific case the equation is therefore 6(y+2.5) = (x-2)²