# Parabola question

• June 8th 2010, 11:58 PM
xsavethesporksx
Parabola question
Given
$x^2-4x=y+4$
Find the vertex, focus and directrix

So i know that i need to complete the square
$x^2-4x+4=y+4+4$

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

Vertex is at $(2,-8)$

and im having a bit of trouble on the focus and directrix....

Thanks
• June 9th 2010, 12:15 AM
xsavethesporksx
okay i figured it out...

$(x-2)^2=a(y+8)$
Since $(y+8)$ doesn't factor, then
$a=1$
general form is $x^2=4ay$
set $4a=1 => a=1/4$

directrix @ $y=-8.25$
focus @ $(2,-7.75)$

(Rock) gotta love when posting on here rings a bell.