Question

write an equation of a parabola with vertex at origin (0,0) with the given focus, and find the directrix. given the focus at (0,-4)

Answer 1

Directrix:

If the vertex of the parabola is at (0, 0) and the focus is (0, -4) which is 4 units down then the directrix will be the line 4 units UP.

Answer: y = 4

Equation of parabola:

$y = \frac{1}{4p}x^{2}$  ; where p is the distance from the vertex to the focus.

As stated above, the focus is 4 units down, so p = -4

$y = \frac{1}{4(-4)}x^{2}$

$y = \frac{1}{-16}x^{2}$

Answer: $y = -\frac{1}{16}x^{2}$