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 $\displaystyle (h, k)$ and the radius as $\displaystyle r$.
To do this in your case, you need to complete the square on $\displaystyle x$ and $\displaystyle y$.
$\displaystyle x^2 + y^2 - 2x - 8y = -1$
$\displaystyle x^2 - 2x + (-1)^2 + y^2 - 8y + (-4)^2 = -1 + (-1)^2 + (-4)^2$
$\displaystyle (x - 1)^2 + (y - 4)^2 = 16$
$\displaystyle (x - 1)^2 + (y - 4)^2 = 4^2$.
So the centre is $\displaystyle (1, 4)$ and the radius is $\displaystyle 4$.