Answer
See explanation.
Work Step by Step
For all points on the $x z$ -plane, we have $y=0$
We can rewrite the equation as $5^{2}=(3+z)^{2}+x^{2}$
This is a sphere of radius 5 centered at (0,0,-3)
(b)
For all points on the $x y$ -plane, we get $z=0$
Substituting $z=0$ gives us $16=x^{2}$
Taking the square root gives us $x=\pm 4$
Thus, the two lines are $-4=x$ and $4=x$
$(c)$
We have all the points on the $yz$ -plane as $x=0$
Replacing (x) with (0) gives us $16=6 z+z^{2}$
\[
-16+6 z+z^{2}=0
\]
\[
(-2+z)(8+z)=0
\]
Thus, the two line are -8=z, 2=z
