Question

How do you find the vertex, focus and directrix of `(x+3)^2=16(y-2)`?

Answer 1

Vertex `(-3, 2)`
Focus `(-3, 6)`
Directrix `y=-2`

Explanation:

From the given
`(x+3)^2=16(y-2)`

This is actually the vertex form, so we can obtain the vertex already
`(x--3)^2=16(y-2)`
`h=-3` and `k=2`

Also `4p=16`
and `p=4`

Focus is at `(-3, 2+4)=(-3, 6)`

Directrix is at `y=2-4=-2`

God bless...I hope the explanation is useful.