Question

How do you find the focus, vertex, and directrix of `x=1/4y^2+2y-2`?

Answer 1

Focus `(-5, -4)`, and Vertex `(-6, -4)` and Directrix `x=-7`

Explanation:

From the given `x=1/4y^2+2y-2`
Multiply by 4
`4x=y^2+8y_8`
Perform completing the square method
`4x=y^2+8y+16-16-8=0`

`4x=(y+4)^2-24`
`(y--4)^2=4(x+6)`
`(y--4)^2=4(x--6)`

it is now in the Vertex Form
`p=1`
Focus `(-5, -4)`, and Vertex `(-6, -4)` and Directrix `x=-7`
graph{(x-1/4y^2-2y+2)(1000000x+y+7(1000000))=0[-20,20,-10,10]}

God bless you ! I hope you find this useful.