Equation of a sphere with given endpoints...

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Hey. Got a question i can't figure out, so i had hoped y'all would know! :)

The problem is that there is a sphere with endpoints P(-3,5,7) and Q(5,-1,5). It asks us to write an equation fro this sphere. what do i do? thanks a bunch!
 
Are we to assume that P(-3,5,7) and Q(5,-1,5) are endpoints of a diameter of the sphere?
If so, the midpoint of PQ is the center of the sphere.
To find the midpoint average the coordinates.
One half the length of PQ is the radius of the shere
 
black0belt0babe7 said:
The problem is that there is a sphere with endpoints P(-3,5,7) and Q(5,-1,5). It asks us to write an equation fro this sphere. what do i do? thanks a bunch!
Spheres don't have end points, sorry. Perhaps you mean they are end points of a diameter? That would work.

Where's the center?

(-3+5)/2 = 2/2 = 1
(5-1)/2 = 4/2 = 2
(7+5)/2 = 12/2 = 6

Center: (1,2,6)

What's the radius?

sqrt((-3-1)<sup>2</sup> + (5-2)<sup>2</sup> + (7-6)<sup>2</sup>) =
sqrt((-4)<sup>2</sup> + (3)<sup>2</sup> + (1)<sup>2</sup>) =
sqrt(16 + 9 + 1) =
sqrt(26)

What's the equation:

(x-1)<sup>2</sup> + (y-2)<sup>2</sup> + (z-6)<sup>2</sup> = 26

Just one piece at a time. No sense fretting over the whole thing at once.
 
yes, i meant that those were the endpoints of the diameter. y'alls posts made me understand it completely....Y'ALL ROCK!

~thanks a ton, Aisha
 
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