Question: Equation of a sphere (5)

Problem 1. Write the equation of the sphere passing through three points A(2, 3, -2), B(-2, 3, 4), C(0, -1, 2) and  tangent to the plane (P): x+5*y+z-33=0.

This is my code

> restart:with(geom3d):

point(A,2,3,-2):

point(B,-2,3,4):

point(C,0,-1,2):

plane(P,x+5*y+z-33=0,[x,y,z]):

point(T,x,y,z):

TA:=distance(T,A):

TB:=distance(T,B):

TC:=distance(T,C):

d:=distance(T,P):

sol:=solve([TA=TB,TA=TC,TA=d],[x,y,z]);

point(T1,subs(sol[1],coordinates(T))):R1:=distance(T1,A):

Eq1:=sort(Equation(sphere(S1,[T1,R1],[x,y,z])));

Student[Precalculus][CompleteSquare](Eq1);

point(T2,subs(sol[2],coordinates(T))):R2:=distance(T2,A):

Eq2:=sort(Equation(sphere(S2,[T2,R2],[x,y,z])));

Student[Precalculus][CompleteSquare](Eq2);

Problem 2. Write the equation of the sphere passing through three points A(0, 2, -2), B(1, 3, 0), C(2, 1, -1) and  tangent to the plane (P): x-y-1= 0.

This is my code

> restart: with(geom3d):

point(A,0,2,-2):

point(B,1,3,0):

point(C,2,1,-1):

plane(P,x-y-1= 0,[x,y,z]):

point(T,x,y,z):

TA:=distance(T,A):

TB:=distance(T,B):

TC:=distance(T,C):

d:=distance(T,P):

sol:=solve([TA=TB,TA=TC,TA=d],[x,y,z]);

point(T1,subs(sol[1],coordinates(T))):R1:=distance(T1,A):

Eq1:=sort(Equation(sphere(S1,[T1,R1],[x,y,z])));

Student[Precalculus][CompleteSquare](Eq1);

Please comment to me. Thank you very much.