Let A(1,-1,-1), B(2,1,2), C(1, 3, 1) be three points and Delta: x = -t, y = -t, z = t be a line. Write the equation of the sphere (S), knowing that center of (S) lies on the line Delta, (S) passing the point A and cuts the plane passing through the three points A, B, C cut (S) a circle has least radius.
This is my code.
> restart;
with(geom3d):
a:=[-t,-t,t]:
point(T,a):
point(A,1,-1,-1):
point(B,2,1,2):
point(C,1,3,1):
plane(ABC,[A,B,C],[x,y,z]):
d:=distance(T,ABC):
R:=distance(T,A):
r:=R^2-d^2;
sol:=minimize(r,'location');
coordinates(point(T1,op(eval(a,op(1,sol[2][1]))))):
rad:=subs(op(1,sol[2][1]),R):
Equation(sphere(S,[T1,rad],[x,y,z])):
Student[Precalculus][CompleteSquare](Equation(S));
Please help me some following questions:
1) I can't use the commant expand(r) or simplify(r).
2) How i can use the commant in the line Student[Precalculus][CompleteSquare](Equation(S));?
3) Please comment to me at the line coordinates(point(T1,op(eval(a,op(1,sol[2][1]))))):
Thank you very much.
