**Find an equation of the sphere that passes through the point (4, 3, 21) and has center (3, 8, 1).**

**Answer:**

so the basic equation of the sphere is

(x-a)^2+(y-b)^2+(z-c)^2 = r^2 where (a,b,c ) is the center of sphere and r is the radius of sphere.

so from given given equation a-3,b=8,c=1

and for r =perpendicular distance between the point(3,8,1) and (4,3,21)

so r^2=(4-3)^2+(3-8)^2+(21-1)^2 =426

so the resulting equation of sphere is

(x-3)^2+(y-8)^2+(z-1)^2=426