Determine an equation of a sphere given that one of the diameters has the extremities: (2,1,4) and (4,3,10)

Question

theeric · Answer

Hi! Do you have the equation for a sphere? Just a general sphere?

theeric · Answer

Also, what kind of coordinate system are you using?

theeric · Answer

This problem might be beyond me.

whpalmer4 · Answer

The distance formula can be extended to a three-dimensional coordinate system:

$$d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$$

You can use that to find the diameter, and then the radius.

Formula for a sphere is $$(x-h)^2+(y-k)^2+(z-l)^2=r^2$$

whpalmer4 · Answer

you know that the center of the sphere must be at the midpoint of that diameter, too...

theeric · Answer

$h$, $k$, and $l$ are the center of the sphere, right?

whpalmer4 · Answer

exactly!

theeric · Answer

$(h,\ k,\ l)$ is the coordinate.
Good luck, @liltish007 !

theeric · Answer

Well, I should probably say $center\ point$ rather than $coordinate$!

whpalmer4 · Answer

and the midpoint of a line is located at the mean of the coordinates of the endpoints.

whpalmer4 · Answer

Actually a pretty easy problem, so long as you know how the familiar equations extend to three dimension!

theeric · Answer

And the midpoint theorem can be extended, just like the distance formula was.

Normally,
$x_{midpoint}=\dfrac{x_2+x_1}{2}$ and $y$ is similiar. Now $z$ is also similar :P

theeric · Answer

I didn't give away too much, did I?

anonymous · Answer

That was all I need :P Thanks:D

whpalmer4 · Answer

What did you get for your result?