Question

What is the equation for a parabola with a focus of (0,-4) and a directrix of y=4 if the vertex is at the origin?..1)..y=1/16x2..2)..x=1/16y2..3)..y=1/32x2..4)..y= -1/16x2.

Answer 1

y = -
`(1)/(16)` x²

Explanation:

Since the vertex is at the origin and the focus at (0, - 4) then the parabola opens vertically down with equation

x² = 4py ( p is the distance from the vertex to the focus )

Here p = - 4 ( focus is below the vertex ), thus

x² = 4(- 4)y = - 16y ( divide both sides by - 16 )

y = -
`(1)/(16)` x²