# Find equation of sphere

1. Feb 28, 2007

### rcmango

1. The problem statement, all variables and given/known data

Find an equation of the sphere one of whose diameters has (1, 3, -5) and
(3, -1, 3) as its endpoints.

2. Relevant equations

midpoint.

3. The attempt at a solution

i don't understand how to find the midpoint, even though its the mean of:
(2, 1, 1)

i've also been given the hint to find the measurement of a great circle:
sqrt( 4 + 16 + 64 ) = sqrt(80)

which equals: Thus,
(x-2) ^ 2 + (y-1) ^ 2 + (z-1) ^ 2 = 80

2. Feb 28, 2007

### dextercioby

I think the center's at (2,1,-1) and from here it follows that the radius is $\sqrt{21}$

3. Feb 28, 2007

### eprjenkins

sqrt( 4 + 16 + 64 ) = sqrt(80)?

Shouldn't it be sqrt( 4 + 16 + 64 ) = sqrt(84)

4. Feb 28, 2007

### HallsofIvy

The midpoint of the line segment from (x0,y0,z0) to (x1,y1,z1) is
$$\left(\frac{x_0+x_1}{2},\frac{y_0+y_1}{2},\frac{z_0+z_1}{2}\right)$$
I thought everyone knew that!
The length of the diameter is $\sqrt{84}= 2\sqrt{21}$.
The length of the radius is half that: $\sqrt{21}$