Question

Find the equation of the parabola with its focus at (0,-4) and its directrix y = 4.

.O A) y=-1/gx²
B) y=1/1072
OC) y = -1/16x²
OD) y = -1/4X²

Answer 1

C) y = (-1/16)x²

Explanation:

I am sure there have been some scanning errors particularly with the answer options.

I am sure "x²" is a factor for the numerators and not for the denominators.

A parabola is the set of all points in a plane that are equidistant between a fixed point (focus) and a line (directrix).

In its simplest form, the parabola with focal length p has its vertex at the origin (0,0) and the focus is at the point (0,p). The directrix is the line y=-p.

in our case, p = -4, as the focus is (0, -4) and the directrix is y = 4.

and we therefore see that the vertex must be at (0, 0).

the standard form for a parabola with vertex at the origin :

x² = 4py

in our case

x² = 4×-4×y = -16y

y = -x²/16 or (-1/16)x²