# Math Help - standard form of circles

1. ## standard form of circles

my problem says find the center & radius os a circle x^2+6x+y^2-4y+4=0

whats the formula i sold my book and im reviewing for my finals

2. Equations of circles are in the form of: $(x-a)^{2} + (y - b)^{2} = r^{2}$
where (a, b) represents your centre of the circle (note the negative signs) and r (not $r^{2}$) represents your radius.

For forms such as your question, you complete the square in respect to each variable:
${\color{blue}x^{2}+6x} + {\color{red}y^{2}-4y+4}=0$
${\color{blue}x^{2} + 6x} + {\color{magenta}\left(\frac{6}{2}\right)^{2}} + {\color{red} (y-2)^{2} } = {\color{magenta}\left(\frac{6}{2}\right)^{2}}$
${\color{blue} (x+9)^{2} } + {\color{red} (y-2)^{2} } = 9$

3. Originally Posted by bharriga

whats the formula i sold my book and im reviewing for my finals