Parabola General to standard form

[markwjak]

Homework Statement

write the standard form of the equation
x^2-4x+8y+12=0
find the focus

Homework Equations

The Attempt at a Solution

i have it down to (x-2)^2=-8(y-8)
i'm not sure if you have to multiply the -8 on the right side of the equations by 4 since the focus is 1/4a

 

[Idyllic]

Homework Statement

write the standard form of the equation
x^2-4x+8y+12=0
find the focus

Homework Equations

The Attempt at a Solution

i have it down to (x-2)^2=-8(y-8)
i'm not sure if you have to multiply the -8 on the right side of the equations by 4 since the focus is 1/4a

(x-2)^2=-8(y-8)

let x' = x-2
let y' = y-8

So, x^2 = -8y'
or y' = -(1/8)*x^2

This is it in standard form. To plot it, the vertex of the parabola will be (2, 8) and it will look like an upside down 'U'.