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September 13th, 2012, 09:12 PM   #1
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Finding the equation of a sphere from a diameter

Hi I am having trouble with the following question

Find the equation of a sphere if one of its diameters has endpoints: (-9, -2, - and (-1, 6, 0).

What I am thinking is that I am supposed to find the diameter using these two vectors and then divide it in half to get the radius i ended up getting the square root of 57
and then use that radius in the sphere equation to try and solve for the Center

i tried plugging in one of the points like so
(-9-h)^2 + (-2-l)^2 + (-8-k)^2 = the square root of 57 squared (so i guess 57)

but now im stuck

Any help would be great
thanks
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September 13th, 2012, 09:22 PM   #2
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Re: Finding the equation of a sphere from a diameter

From the given end-points of the diameter, we find square of the radius r is:

\)^2\)=48" />

The center of the sphere will be the mid-point of the diameter:



Hence, the equation of the sphere is:

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September 13th, 2012, 09:31 PM   #3
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Re: Finding the equation of a sphere from a diameter

Thanks a lot
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