# Math Help - Finding the center and radius of an equation

1. ## Finding the center and radius of an equation

x^2 + y^2 - 2x - 8y = -1

Can anyone thoroughly explain how to find the center and radius?

2. Originally Posted by emidavis
x^2 + y^2 - 2x - 8y = -1

Can anyone thoroughly explain how to find the center and radius?
You need to get it to the form

[mth](x - h)^2+ (y - k)^2 = r^2[/tex].

Then you can read off the centre as $(h, k)$ and the radius as $r$.

To do this in your case, you need to complete the square on $x$ and $y$.

$x^2 + y^2 - 2x - 8y = -1$

$x^2 - 2x + (-1)^2 + y^2 - 8y + (-4)^2 = -1 + (-1)^2 + (-4)^2$

$(x - 1)^2 + (y - 4)^2 = 16$

$(x - 1)^2 + (y - 4)^2 = 4^2$.

So the centre is $(1, 4)$ and the radius is $4$.