Answer
$${\text{Single point }}\left( {1, - 3,0} \right)$$
Work Step by Step
$$\eqalign{
& {x^2} - 2x + {y^2} + 6y + {z^2} + 10 = 0 \cr
& {\text{Group terms}} \cr
& \left( {{x^2} - 2x} \right) + \left( {{y^2} + 6y} \right) + {z^2} = - 10 \cr
& {\text{Complete the square}} \cr
& \left( {{x^2} - 2x + 1} \right) + \left( {{y^2} + 6y + 9} \right) + {z^2} = - 10 + 1 + 9 \cr
& {\left( {x - 1} \right)^2} + {\left( {y + 3} \right)^2} + {z^2} = 0 \cr
& {\text{The equation is in the form }}{\left( {x - a} \right)^2} + {\left( {y - b} \right)^2} + {\left( {z - c} \right)^2} = {r^2} \cr
& {\text{because }}r = 0,{\text{ the equation represents a point at }}\left( {a,b,c} \right) \cr
& {\text{Single point }}\left( {1, - 3,0} \right) \cr} $$
