Answer
center $(5, -1, -4)$, radius $\sqrt{51}$
Work Step by Step
$x^2+y^2+z^2-10x+2y+8z=9$
$x^2-10x+y^2+2y+z^2+8z=9$
$x^2-10x+(\frac{-10}{2})^2+y^2+2y+(\frac{2}{2})^2+z^2+8z+(\frac{8}{2})^2=9+(\frac{-10}{2})^2+(\frac{2}{2})^2+(\frac{8}{2})^2$
$x^2-10x+25+y^2+2y+1+z^2+8z+16=9+25+1+16$
$(x-5)^2+(y+1)^2+(z+4)^2=51$
This is a sphere with center $(5, -1, -4)$ and radius $\sqrt{51}$.
