Answer: The equation of the sphere is:
(x-2)^2 + (y-2)^2 + (z-5/2)^2 = sqrt(245)/2
Step-by-step explanation:
The centre of the sphere is the midpoint of the diameter, which is
1/2
[(-4,7,6) + (8,-3,5)] =(2,2,5/2)
The length of the diameter is
=sqrt |(8,-3,5) - (-4,7,6)|^2
=sqrt (12^2 + (-10)^2 + (-1)^2)
=sqrt (144+100+1)
=sqrt(245)
so the radius of
the sphere is:
1/2(sqrt(245)) = sqrt(245)/2.
The equation of the sphere is:
(x-2)^2 + (y-2)^2 + (z-5/2)^2 = sqrt(245)/2
