1.

Find the equation of the sphere passing through (0, 0, 0), (1, 0, 0) and (0, 0, 1).

Answer» Let the equation of the sphere be
`" "x^(2)+y^(2)+z^(2)+2ux+2vy+2wx=0" "`(i)
As (i) passes through (0, 0, 0), (1, 0, 0), (0, 1, 0) and (0, 0, 1), we must have `d=0, 1+2u+d=0`
`1+2v+d=0 and 1+2w+d=0`
Since `d=0`, we get `2u=2v=2w=-1`
Thus, the equation of the required sphere is `x^(2)+y^(2)+z^(2)-x-y-z=0`


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