Question

Co-ordinates of a point equidistant from the points (0,0,0), (a, 0, 0), (0, b, 0), (0, 0, c) is

• A.
  
• B.
  
• C.
  
• D. (a, b, c)

Answer 1

The correct option is C

The required point is the centre of the sphere through the given points. Let the equation of sphere be
$x^2+y^2+2ux+2vy+2wz+d=0\cdots \left(i\right)$
Sphere (i) is passing through (0,0,0), (a,0,0),(0,b,0) and (0,0,c), $\therefore$ d = 0
$a^2+2ua+0\Rightarrow u=-\frac{a}{2}{b}^2+2vb=0\Rightarrow v=-\frac{b}{2}{c}^2+2wc=0\Rightarrow w=-\frac{c}{2}$
Therefore, centre of sphere is $(\frac{a}{2},\frac{b}{2},\frac{c}{2})$, which is also the required point.