Question

lf $(u,v,w)$ be the centre of the sphere which passes through the points $(0,0,0),(0,2,0),(1,0,0)$ and$(0,0,4)$, then $u+v+w=$

• A. $\frac{3}{2}$
• B. $\frac{5}{2}$
• C. $\frac{7}{2}$
• D. $\frac{9}{2}$

Answer 1

The correct option is C $\frac{7}{2}$

Equation of sphere passes through origin is given by,
$x^2+y^2+z^2+ax+by+cz=0$
Given, it also passes through $(0,2,0),(1,0,0),(0,0,4)$
$4++2b=0\Rightarrow b=-2$
$1+a=0\Rightarrow a=-1$
and $16+4c=0\Rightarrow c=-4$
Therefore, the centre of the sphere is $(\frac{1}{2},1,2)$
Ergo $u+v+w=\frac{7}{2}$