The equation of the sphere (S) is given as x^2 + y^2 + z^2 - 2x - 2y - 2z - 1 = 0.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Analyze the sphere equation.
The equation of the sphere $(S)$ is given as $x^2 + y^2 + z^2 - 2x - 2y - 2z - 1 = 0$.
To find the center and radius, we complete the square for each variable:
$$ (x^2 - 2x) + (y^2 - 2y) + (z^2 - 2z) = 1 $$
Add $(1)^2$ to complete the square for each term:
$$ (x^2 - 2x + 1) + (y^2 - 2y + 1) + (z^2 - 2z + 1) = 1 + 1 + 1
