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undrcvrbro
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Homework Statement
Find the equation of a sphere if one of its diameters has endpoints: (-1, -16, -1) and (17, 2, 17).
Homework Equations
midpoint formula= x1+x2/2 + y1+y2/2 + z1+z2/2
equation of a sphere= (x-a)^2 +(y-b)^2 +(z-c)^2
The Attempt at a Solution
Okay this problem is driving me nuts. It seems so simple and I keep goofing it up somehow.
First, the magnitude of the diameter:
=[tex]\sqrt{(17-(-1))^2 + (2-(-16))^2 + (17-(-1))^2}[/tex]
=[tex]\sqrt{972}[/tex]
Radius= (1/2)diameter
=[tex]\sqrt{972}/2[/tex]
So I think this is where I'm confusing things. For the coordinates I used to mid point formula:
[tex]\frac{(-1)-17}{2}=3[/tex]
[tex]\frac{(-16)-2}{2}=-7[/tex]
[tex]\frac{(-1)-17}{2}=8[/tex]
So then plugging into the equation of a sphere...
(x-3)^2 + (y+7)^2 + (z-8)^2 = (15.588)^2
They want the entire equation equal to zero
(x-3)^2 + (y+7)^2 + (z-8)^2 - 243 = 0
But apparently this answer is wrong. Where did I go wrong? I've gone through this problem multiple times and I can't figure it out.