Question

Derive the equation of the parabola with a focus at (0, −4) and a directrix of y = 4

Answer 1

i got f(x) = −1/16 x^2 ,not sure though

Answer 2

`y' = (-x)/(8)`.

Explanation:

The formula to find the equation of a parabola with the focus and the directrix is
`(x-a)^(2)+b^(2)-c^(2)= 2(b-c)y` where (a,b) is the vertex and y=c is the directrix. So the equation is

`(x-0)^(2)+(-4)^(2)-4^(2)= 2(-4-4)y`

`x^(2)+16-16= 2(-8)y`

`x^(2)= -16y`

`y = (-x^(2))/(16)`

Then, the derivated equation is

`y' = (-2x)/(16)`

`y' = (-x)/(8)`.