Correct Answer - Option 3 : 7

__Concept__:

The general equation of sphere is x^{2} + y^{2} + z^{2} + 2ux + 2vy + 2wz + d = 0 with centre at (-u, -v, -w) and radius \(r = \sqrt {{u^2} + {v^2} + {w^2} - d}\)

__Calculation__:

Given: x^{2} + y^{2} + z^{2} – 6x + 8y – 10z + 1 = 0 represents a sphere.

Now, by comparing the given equation of sphere with the general equation of sphere x^{2} + y^{2} + z^{2} + 2ux + 2vy + 2wz + d = 0, we get: u = -3, v = 4, w = -5 and d = 1.

As we know that, for a sphere x^{2} + y^{2} + z^{2} + 2ux + 2vy + 2wz + d = 0 the centre is (- u, - v, - w) and radius \(r = \sqrt {{u^2} + {v^2} + {w^2} - d}\)

\(r = \sqrt {{u^2} + {v^2} + {w^2} - d} = \sqrt {{{\left( { - \;3} \right)}^2} + {4^2} + {{\left( { - \;5} \right)}^2} - 1} = 7\)