What is the equation? focus: (-2, 8) and directrix at y= -4?

Answer 1

The vertex lies equidistant between focus and directrix in a parabola. A quick visual aid will help you see 2 things: the parabola opens up (away from the directrix) and the vertex is at (-2,2). So the equation is:

4p(y-2) = (x+2)², where p is the distance from vertex to focus.

Since p = 6, we have

24(y-2) = (x+2)²

Answer 2

(x+2)^2+(y-8)^2 = (y+4)^2 ( the definition of a PARABOLA

x^2+4x+4+y*^2-16y+64= y^2+8y+16 so
24 y= x^2+4x+52