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 = -2x b)y2 = -8x c)y equals negative 1 divided by 8 x squared d)y equals negative 1 divided by 2 x squared find 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 squared b)y2 = 16x c)16y = x2 d)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 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 and a directrix at

Which is the between a point in the parabola and the focus
 
Which is the distance from the directrix to a point in the parabola. Then knowing that both must be equal we get:

Applying the squares at both sides and noting that we have:

Which is the equation of the parabola. The first answer is C).
For the second one we have:

Simplifying in a similar manner as before we get:
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.

Answer choices