Correct Answer - Option 1 : x

^{2} + y

^{2} + z

^{2} + 4x – 6y – 8z = 7

__Concept:__

- General equation of a sphere cantered at the point (x
_{0}, y_{0}, z_{0}) with radius R is given by
- (x – x
_{0})^{2} + (y – y_{0})^{2} + (z – z_{0})^{2} = R^{2}

__Calculation:__

Given: Centre is at (-2, 3, 4) and radius is 6

⇒ (x_{0}, y_{0}, z_{0}) = (-2, 3, 4) and R = 6

We know that general equation of sphere is (x – x_{0})^{2} + (y – y_{0})^{2} + (z – z_{0})^{2} = R^{2}

⇒ (x – (-2))^{ 2} + (y – 3)^{2} + (z – 4)^{2} = 6^{2}

⇒ (x + 2)^{ 2} + (y – 3)^{2} + (z – 4)^{2} = 6^{2}

⇒ x^{2} + 4x + 4 + y^{2} – 6y + 9 + z^{2} – 8z + 16 = 36

⇒ x^{2} + y^{2} + z^{2} + 4x – 6y – 8z + 29 = 36

⇒ x^{2} + y^{2} + z^{2} + 4x – 6y – 8z = 7

∴ Option 1 is correct.