Doubts with the response

To determine the equation of the sphere that passes in A and B, and has straight center in s

(s):

My solution:

For the straight, center:

The equation is:

BUT THE ANSWER IS:

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- Sep 5th 2008, 07:26 AMApprentice123spherical
Doubts with the response

To determine the equation of the sphere that passes in A and B, and has straight center in s

(s):

My solution:

For the straight, center:

The equation is:

BUT THE ANSWER IS:

- Sep 5th 2008, 08:04 AMLaurent
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.

Laurent. - Sep 5th 2008, 10:20 AMPlato
Each of the points is the same distance from the center.

So solve .

If correct, you will find z=1.

Then you can find x&y on s. - Sep 5th 2008, 10:28 AMLaurent
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. - Sep 5th 2008, 10:31 AMPlato
- Sep 5th 2008, 10:42 AMLaurent
Well done, Plato ! This is indeed quicker to write down this way.

- Sep 6th 2008, 11:29 AMApprentice123
thanks