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

equation-of-sphere

#1

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