Correct Answer - Option 4 : Infinite
Concept used:
The general equation of a sphere is (x - a)2 + (y - b)2 + (z - c)2 = r2, where (a, b, c) represents the center of the sphere, 'r' represents the radius, and x, y, and z are the coordinates of the points on the surface of the sphere.
Equation of sphere is
x2 + y2 + z2 + 2ux + 2vy + 2wz + d = 0
also it passes through (1, 0, 0), (0, 1, 0) and (0, 0, 1)
when the sphere passes through (1, 0, 0) we get
x2 + y2 + z2 + 2ux + 2vy + 2wz + d = 0
12 + 0 + 0 + 2u + 0 + 0 + d = 0
1 + 2u + d = 0
2u + d = -1
When the sphere passes through (0, 1, 0) we get
x2 + y2 + z2 + 2ux + 2vy + 2wz + d = 0
0 + 12 + 0 + 0 + 2v + 0 + d = 0
1 + 2v + d = 0
2v + d = -1
Similarly, when the sphere passes through (0, 0, 1) we get
x2 + y2 + z2 + 2ux + 2vy + 2wz + d = 0
0 + 0 + 1 + 0 + 0 + 2w + d = 0
1 + 2w + d = 0
2w + d = -1
Cleary we can see that all the equation depends on the diameter, so there can be infinite no of sphere passing through these points.
