PLEASE HELP 20 POINTS IF ITS CORRECT WILL MARK BRAINLIEST Find the standard form of the equation of the parabola with a focus at (0, -2) and a directrix at y = 2.A)y2 = -2xB)y2 = -8xC)y equals negative 1 divided by 8 x squaredD)y equals negative 1 divided by 2 x squaredFind the standard form of the equation of the parabola with a focus at (-8, 0) and a directrix at x = 8.A)y equals negative 1 divided by 32 x squaredB)y2 = 16xC)16y = x2D)x equals negative 1 divided by 32 y squared

For the first parabola we have a focus at (0,-2) and a directrix at y=2. Remember that the distance between any point [tex](x,y)[/tex] in the parabola and the focus must be equal to the distance between that point in the parabola and the directrix. Knowing this we will have for a focus at [tex](x_f,y_f)[/tex] and a directrix at [tex]y_d=c[/tex]
[tex] \sqrt{(x-x_f)^2+(y-y_f)^2} [/tex]
Which is the between a point in the parabola and the focus
[tex]|y-c|[/tex] 
Which is the distance from the directrix to a point in the parabola. Then knowing that both must be equal we get:
[tex]\sqrt{(x-x_f)^2+(y-y_f)^2}=|y-c|\implies \sqrt{(x-0)^2+(y+2)^2}=|y-2|[/tex]
Applying the squares at both sides and noting that [tex](|x|)^2=x^2[/tex] we have:
[tex](x-0)^2+(y+2)^2=(y-2)^2\implies x^2+y^2+4+4y=y^2+4-4y \\ \\ \implies x^2+4y=-4y\implies y=-\frac{x^2}{8}[/tex]
Which is the equation of the parabola. The first answer is C).
For the second one we have:
[tex]\sqrt{(x-+8)^2+(y)^2}=|x-8|\implies(x-+8)^2+(y)^2=(x-8)^2[/tex]
Simplifying in a similar manner as before we get:
[tex]x=-\frac{y^2}{32}[/tex] The answer is D.
Note that this time the parabola will be sideways with it's vertex on the origin and opening in the negative x direction.