Doubts with the response
To determine the equation of the sphere that passes in A and B, and has straight center in s
For the straight, center:
The equation is:
BUT THE ANSWER IS:
How did you find the center ? It is supposed to lie on the line S, so it must satisfy both equations, which it does'nt.
The center must be equidistant from A and B, and satisfy the two equations. This makes 3 equations, allowing you to find the three components of the center.
How do you get this equation, Plato ?
A and B are at the same distance from the center O, so the coordinates of the center satisfy:
Expand this. The squares simplify, so you get a linear equation. The equations of S provide two others, and you have a linear system of three equations in three unknowns.