Question

Number of spheres drawn through the points $(0,0,0),($1, $0,0),(2,3,-9),(-3,0,0)$ are

• A. $0$
• B. $1$
• C. $2$
• D. Infinite

Answer 1

The correct option is B $1$

Equation of sphere passes through origin is given by,
$x^2+y^2+z^2+ax+by+cz=0$
Given, it also passes through $(1,0,0),(2,3,-9),(-3,0,0)$
$1+a=0\Rightarrow a=-1$
and $9-3c=0\Rightarrow c=3$
$4+9+81+2a+6b-18c=0$

$\Rightarrow 94-2+6b-54=0$

$\Rightarrow b=38$
Hence, equation of the sphere is
$x^2+y^2+z^2-x+38y+3z=0$
Therefore, the number of possible sphere through given points is $1$.