MaplePrimes - answers and comments on Question, Equation of a sphere (1)

2) How i can use the commant sort

toandhsp — Mon, 13 Feb 2012 19:43:28 Z

2) How i can use the commant sort in the line Student[Precalculus][CompleteSquare](Equation(S));?

Another version of your code

Kitonum — Mon, 13 Feb 2012 22:19:49 Z

I would write your code so:

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; simplify(r) assuming real;

sol:= minimize(r, location); Sol:= op(sol[2])[1];

point(T, subs(Sol, a)): R:= subs(Sol, R):

Equation(sphere(S, [T,R], [x, y, z]));

Eq:=Student[Precalculus][CompleteSquare](Equation(S));

op(1, Eq) - op(4, op(1, Eq)) = sqrt(-op(4, op(1, Eq)))^`2`; # Canonical equation of S

Here you will find answers to your questions!

Thank you

toandhsp — Tue, 14 Feb 2012 11:34:17 Z

Thank you very much. I want the anserw has the form (x+1)^2 + (y+1)^2 + (z-1)^2 = (2*2^(1/2))^`2` not the form (z-1)^2+(y+1)^2+(x+1)^2 = (2*2^(1/2))^`2`. What must i do?

Answer

Kitonum — Tue, 14 Feb 2012 21:10:47 Z

I have not found a suitable way to sort, so I suggest a way to manually isolate complete squares.

The 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; simplify(r) assuming real;

sol:= minimize(r, location); Sol:= op(sol[2])[1];

point(T, subs(Sol, a)): R:= subs(Sol, R):

Eq:=lhs(Equation(sphere(S, [T,R], [x, y, z])));

(x+coeff(Eq,x)/2)^2+(y+coeff(Eq,y)/2)^2+(z+coeff(Eq,z)/2)^2=sqrt((coeff(Eq,x)^2+coeff(Eq,y)^2+coeff(Eq,z)^2)/4-tcoeff(Eq))^`2`; # Canonical equation of S