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What is the radius of the sphere x2 + y2 + z2 – 6x + 8y – 10z + 1 = 0?
1. 5
2. 2
3. 7
4. 3
5. None of these

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Correct Answer - Option 3 : 7

Concept:

The general equation of sphere is x2 + y2 + z2 + 2ux + 2vy + 2wz + d = 0 with centre at (-u, -v, -w) and radius \(r = \sqrt {{u^2} + {v^2} + {w^2} - d}\)

Calculation:

Given: x2 + y2 + z2 – 6x + 8y – 10z + 1 = 0 represents a sphere.

Now, by comparing the given equation of sphere with the general equation of sphere x2 + y2 + z2 + 2ux + 2vy + 2wz + d = 0, we get: u = -3, v = 4, w = -5 and d = 1.

As we know that, for a sphere x2 + y2 + z2 + 2ux + 2vy + 2wz + d = 0 the centre is (- u, - v, - w) and radius \(r = \sqrt {{u^2} + {v^2} + {w^2} - d}\)

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

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