Question

Number of spheres drawn through the points $(0,0,0),(1,0,0),(0,1,0),(1,1,0)$ are

• A. $0$
• B. $5$
• C. Infinite
• D. $2$

Answer 1

The correct option is C Infinite

Equation of sphere passing through $(0,0,0)$ is given by,
$x^2+y^2+z^2+2ux+2vy+2wz=0$
Also it passes through $(1,0,0),(0,1,0),(1,1,0)$
$\Rightarrow 2u+1=0\Rightarrow 2u=-1$
$1+2v=0\Rightarrow 2v=-1$
and $2+2u+2v=0$
Clearly $u=v=-\frac{1}{2}$ and $w$ can have any value. Hence, there can be infinite sphere which will pass through given points.