Write an equation of the parabola with focus f(0,-3) and directrix y=3

check the picture below, so the parabola looks more or less like so.

bearing in mind that the vertex is half-way between the directrix and the focus point, so that puts it in the origin.

the distance from the vertex to the directrix or focus point is "p" units, in this case, just 3 units, however, the parabola is opening downwards, meaning "p" is negative, so p = -3.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

it would open into a square depending on the type of envelope i’m not sure about the second part