Q221 / 270 · NDA 2012 (Phase 1) · Mathematics
What is the diameter of the sphere $x^2+y^2+z^2-4 x+$ $6 y-8 z-7=0$
- A4 units
- B5 units
- Correct answerC6 units
- D12 units
Solution
Compare with
$\begin{aligned}
& x^2+y^2+z^2+2 u x+2 v y+2 w z+d=0 \\
& u=-2, v=3, w=-4, d=-7 \\
& \text { radius }=\sqrt{u^2+v^2+w^2-d} \\
& =\sqrt{4+9+16+7} \\
& =\sqrt{36}=6 .
\end{aligned}$
Hence, the correct answer is option: 'C'.