The coordinates of a point which is equidistant from the points (0, 0, 0), (o, 0, 0), (0, b, 0), (0,0, c) are given by

Let P be any point in a space. According to the given condition, (x−0)2+(y−0)2+(z−0)2=(x−a)2+y2+z2=x2+(y−b)2+z2=x2+y2+(z−c)2On squaring both sides, we get  x2+y2+z2=(x−a)2+y2+z2=x2+(y−b)2+z2=x2+y2+(z−c)2⇒ x2+y2+z2=x2+a2−2ax+y2+z2⇒  a2−2ax=0⇒ x=a2Similarly, we can solve the other values, we gety=b2,z=c2