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 = (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 = (1)/(4(-4))x^(2)`

`y = (1)/(-16)x^(2)`

Answer:
`y = -(1)/(16)x^(2)`