<p>The centre of the sphere <span class="math">(x-4)(x+4) + (y-3)(y+3) + z^2 = 0</span> is</p>
Step-by-Step Solution
Key Concept: Expand the products and identify the standard form of a sphere equation to find the centre.
Step 1: Expand the equation. \((x-4)(x+4) + (y-3)(y+3) + z^2 = 0\) \(x^2 - 16 + y^2 - 9 + z^2 = 0\) \(x^2 + y^2 + z^2 = 25\) Step 2: This is in the form \(x^2 + y^2 + z^2 = r^2\), which has centre at \((0, 0, 0)\). ∴ Answer is (c).
Correct Answer: C