Question

Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = −1.

f(x) = -1/4 x^2
f(x) = 1/4 x^2
f(x) = −4x^2
f(x) = 4x^2

Answer 1

ok, so from previous question
(x-h)^2=4p(y-k)

distance from focus to directix is 2
2/2=1=p
1>-1
focus is above the vertex
1 unit down from (0,1) is (0,0)
vertex at (0,0)
since focus is above, p is positive


(x-0)^2=4(1)(y-0)
x^2=4y
4y=x^2
divide both sides by 4
y=(1/4)x^2
f(x)=1/4x^2

2nd one is answer