Question

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

Answer 1

Answer:

$y' = \frac{-x}{8}$.

Step-by-step 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

$(x-0)^{2}+(-4)^{2}-4^{2}= 2(-4-4)y$

$x^{2}+16-16= 2(-8)y$

$x^{2}= -16y$

$y = \frac{-x^{2}}{16}$

Then, the derivated equation is

$y' = \frac{-2x}{16}$

$y' = \frac{-x}{8}$.

Answer 2

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