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Find equation of sphere

  • Thread starter rcmango
  • Start date
  • #1
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Homework Statement



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

Homework Equations



midpoint.

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

please help me solve this problem, i almost got it!
 

Answers and Replies

  • #2
dextercioby
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I think the center's at (2,1,-1) and from here it follows that the radius is [itex] \sqrt{21} [/itex]
 
  • #3
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sqrt( 4 + 16 + 64 ) = sqrt(80)?

Shouldn't it be sqrt( 4 + 16 + 64 ) = sqrt(84)
 
  • #4
HallsofIvy
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The midpoint of the line segment from (x0,y0,z0) to (x1,y1,z1) is
[tex]\left(\frac{x_0+x_1}{2},\frac{y_0+y_1}{2},\frac{z_0+z_1}{2}\right)[/tex]
I thought everyone knew that!
The length of the diameter is [itex]\sqrt{84}= 2\sqrt{21}[/itex].
The length of the radius is half that: [itex]\sqrt{21}[/itex]
 

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