Question

find the general equation of the sphere with the following points on diameter, (-1,2,5) and (3,6,1)

Answer 1

in 2d, the equation of a circles is
(x-h)^2 + (y-k)^2 = r^2

the same concept holds true in 3-d
(x-i)^2 + (y-j) ^2 + (z-k)^2 = r^2

find the midpoint of those 2 points, that would be your center.
find the disance from the center to one of those points on the diameter, that is your radius,