Question

Find the standard form of the equation of the parabola with a focus at (0, 5) and a directrix at y = -5.

Answer 1

find the equation for the following parabola.

focus: ( 0, 5 )

directrix: y = -5

correct answer: x ² = 20 y

Answer 2

The focus-directrix form of a parabola is (x - h)² = 4p (y - k), where the focus is (h, k + p) and the directrix is y = k - p.
in this case,
h=0
k+p=5
k-p=-5
solve for p and k: (k+p)+(k-p)=5+(-5), 2k=0, k=0, p=5
(x-0)²=4*5(y-0), x²=20y
so the standard form of a parabola is y=ax²+bx+c
in this case, it is :y=(1/20)x²