Find the coordinates of the point equidistant from the points `(0,0,0),(2,0,0),(0,4,0) and (0,0,6)`

Options

A. (1,2,3)
B. (2,3,1)
C. (3,1,2)
D. (1,3,2)

Answer

A

Explanation

The equation of sphere passing through the given points is
`x^2+y^2+z^2+2ux+2vy+2wz+d=0`
`:' (0)^2+(0)^2+(0)^2+2u(2)+2v(0)+2w(0)+d=0`
`rArr d=0`
`(2)^2+(0)^2+(0)^2+2u(2)+(2v(0)+(2w(0)+0=0`
`rArr u=-1`
`(0)^2+(4)^2+(0)^2+2u(0)+2v(4)+2w(0)+0=0`
`rArr v=-2`
and
`(0)^2+(0)^2+(6)^2+2u(0)+2v(00+2w(6)+0=0`
`rArr w=-3`
`:." The centre of sphere "=(1,2,3)`
It will be the point equidistant from the four points (0,0,0),(2,0,0),(0,4,0) and (0,0,6).