The general equation of the sphere centered at (a,b,c) with radius r is:
(x-a)^2 + (y-b)^2 + (z-c)^2 = r^2.
In this case we have (x-5)^2 + (y-8)^2 + (z-3) = r^2.
We know that the point (7, 5, -3) satisfies this equation. Subbing those three coordinates in the above equation will enable us to determine the radius, r:
(7-5)^2 + (5-8)^2 + (-3-3)^2 = r^2. Then:
4 + 9 + 36 = r^2. r^2 is then 49, and the radius, r, must then be +7.
In summary, the equation of the given sphere is:
(x-5)^2 + (y-8)^2 + (z-3)^2 = 7^2.
