Answer
Sphere.
Work Step by Step
Surface equation is
\[
-2 x-6 y-8 z+x^{2}+y^{2}+z^{2}+10
\]
Group terms
\[
\begin{array}{c}
25=9+16=\left(-2 x+x^{2}+1\right)+\left(-8 z+z^{2}+16\right)+\left(-6 y+y^{2}+9\right)\\
\Rightarrow5^{2}=(-4+z)^{2}+(-3+y)^{2}+(-1+x)^{2}
\end{array}
\]
And therefore the given surface represents a sphere with center (1,3,4) and radius 5.
