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 September 13th, 2012, 09:12 PM #1 Newbie   Joined: Sep 2012 Posts: 10 Thanks: 0 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
 September 13th, 2012, 09:22 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs 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: $r^2=\frac{1}{4}$$\(-1-(-9)$$^2+$$6-(-2)$$^2+$$0-(-$$^2\)=48" /> The center of the sphere will be the mid-point of the diameter: $(h,k,l)=$$\frac{-9-1}{2},\frac{-2+6}{2},\frac{-8+0}{2}$$=$$-5,2,-4$$$ Hence, the equation of the sphere is: $$$x+5$$^2+$$y-2$$^2+$$z+4$$^2=48$
 September 13th, 2012, 09:31 PM #3 Newbie   Joined: Sep 2012 Posts: 10 Thanks: 0 Re: Finding the equation of a sphere from a diameter Thanks a lot

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# equation of sphere at end of diameter

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