UPSC NDA II 2014 Mathematics Paper

Let equation of a sphere be
(x−a)2+(y−b)2+(z−c)2=r2
If the origin and given points lie on the sphere, then
a2+b2+c2=r2......(1)
From 1 and 2
2a+b−c=3...(5)
From 1 and 3
a+5b−4c=21....(6)
From 1 and 4
−a+2b−3c=14....(7)
By inspection, the point (−1,2,−3) satisfies the above equations 5,6 and 7