Algebra 2 (Conic Sections)..help?

Question

Q: Equation for each prabola.

focus (-4,-2)
Dicrectix x= -8

Answer 1

Find the equation of the parabola with

Focus: (-4, -2)
Directrix: x = -8

The directrix is a vertical line so the parabola is horizontal.
The directed distance from the directrix to the focus is 2p.

2p = -4 - (-8) = - 4 + 8 = 4
p = 2
4p = 8

The directed distance from the vertex to the focus is p.

The x coordinate of the vertex is:

-4 - p = -4 - 2 = -6

The vertex is (h, k) = (-6, -2).

The equation of the parabola is:

4p(x - h) = (y - k)²
8(x + 6) = (y + 2)²

Answer 2

Given the focus(a,b) and the directrix(c) the eqn of parabola is,

(y - b)^2 = -2(c-a)(x - (a+c)/2)

(y + 2)^2 = -2(-4)(x + 6)
(y + 2)^2 = 8 (x + 6)