Answer
The surface corresponds to a sphere of radius $r=7$ and is concentrated at $C(-5,-2,-1)$
Work Step by Step
There is given a surface
\[
0=10 x+4 y+2 z-19+x^{2}+y^{2}+z^{2}
\]
By completing squares:
\[
\begin{aligned}
&0= 4 y+2 z-19+10 x+ x^{2}+y^{2}+z^{2}\\
\Rightarrow &\left(2 z+1+z^{2}\right)-25-4-1-19+\left(25+ 10 x+x^{2}\right)+\left(4+4y+y^{2}\right)=0 \\
\Rightarrow &49=(2+y)^{2}+(1+z)^{2}+(5+x)^{2} \\
\Rightarrow &7^{2}=(1+z)^{2}+(2+y)^{2}+(5+x)^{2}
\end{aligned}
\]
This surface corresponds to a sphere of radius $r=7$ and is concentrated at
\[
C(-5,-2,-1)
\]
