Revisions to How do I get my equation to have the form $(x-a)^2 + (y-b)^2 + (z-c)^2-d = 0$?

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edited May 21, 2013 at 11:34

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SolveAlways[{-11 -eq 2= (x + x^2 - 4 ya)^2 + y^2(y - 6b)^2 + (z +- c)^2 z^2- ==d;
sol (x= SolveAlways[{-11 a)^2- 2 x + (yx^2 - b)^24 y + (zy^2 - c)^26 -z 25+ z^2 == eq}, {x, y, z}]
eq /. sol // PolynomialForm[#, TraditionalOrder -> True] &

(* {{d -> 25, a -> 1, b -> 2, c -> 3}} *)

Updated:

(* {(x-1)^2+(y-2)^2+(z-3)^2-25} *)


eq = (x - a)^2 + (y - b)^2 + (z - c)^2 - d;
solSolve[ForAll[{x, =y, SolveAlways[{z}, -11 - 2 x + x^2 - 4 y + y^2 - 6 z + z^2 == eq}eq], {xa, yb, z}]
eq /. sol // PolynomialForm[#c, TraditionalOrder -> True] &d}]

(* {{d -> 25, a -> 1, b -> 2, c -> 3}}, *)
(*d {(x-1)^2+(y-2)^2+(z-3)^2-> 25} }*)

SolveAlways[{-11 - 2 x + x^2 - 4 y + y^2 - 6 z +  z^2 ==
 (x - a)^2 + (y - b)^2 + (z - c)^2 - 25}, {x, y, z}]
(*{{a -> 1, b -> 2, c -> 3}}*)

Updated:

eq = (x - a)^2 + (y - b)^2 + (z - c)^2 - d;
sol = SolveAlways[{-11 - 2 x + x^2 - 4 y + y^2 - 6 z + z^2 == eq}, {x, y, z}]
eq /. sol // PolynomialForm[#, TraditionalOrder -> True] &

(* {{d -> 25, a -> 1, b -> 2, c -> 3}} *)
(* {(x-1)^2+(y-2)^2+(z-3)^2-25} *)

eq = (x - a)^2 + (y - b)^2 + (z - c)^2 - d;
sol = SolveAlways[{-11 - 2 x + x^2 - 4 y + y^2 - 6 z + z^2 == eq}, {x, y, z}]
eq /. sol // PolynomialForm[#, TraditionalOrder -> True] &

(* {{d -> 25, a -> 1, b -> 2, c -> 3}} *)
(* {(x-1)^2+(y-2)^2+(z-3)^2-25} *)


eq = (x - a)^2 + (y - b)^2 + (z - c)^2 - d;
Solve[ForAll[{x, y, z}, -11 - 2 x + x^2 - 4 y + y^2 - 6 z + z^2 == eq], {a, b, c, d}]

(*{{a -> 1, b -> 2, c -> 3, d -> 25}}*)

added 175 characters in body

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edited Feb 25, 2013 at 11:32

chyanog

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83

SolveAlways[{-11 - 2 x + x^2 - 4 y + y^2 - 6 z +  z^2 ==
 (x - a)^2 + (y - b)^2 + (z - c)^2 - 25}, {x, y, z}]
(*{{a -> 1, b -> 2, c -> 3}}*)

Updated:

eq = (x - a)^2 + (y - b)^2 + (z - c)^2 - d;
sol = SolveAlways[{-11 - 2 x + x^2 - 4 y + y^2 - 6 z + z^2 == 
(x - a)^2 + (y - b)^2 + (z - c)^2 - deq}, {x, y, z}]
eq /. sol // PolynomialForm[#, TraditionalOrder -> True] &

(* {{d -> 25, a -> 1, b -> 2, c -> 3}} *)
(* {(x-1)^2+(y-2)^2+(z-3)^2-25} *)

SolveAlways[{-11 - 2 x + x^2 - 4 y + y^2 - 6 z +  z^2 ==
 (x - a)^2 + (y - b)^2 + (z - c)^2 - 25}, {x, y, z}]
(*{{a -> 1, b -> 2, c -> 3}}*)

Updated:

SolveAlways[{-11 - 2 x + x^2 - 4 y + y^2 - 6 z + z^2 == 
(x - a)^2 + (y - b)^2 + (z - c)^2 - d}, {x, y, z}]

(*{{d -> 25, a -> 1, b -> 2, c -> 3}}*)

SolveAlways[{-11 - 2 x + x^2 - 4 y + y^2 - 6 z +  z^2 ==
 (x - a)^2 + (y - b)^2 + (z - c)^2 - 25}, {x, y, z}]
(*{{a -> 1, b -> 2, c -> 3}}*)

Updated:

eq = (x - a)^2 + (y - b)^2 + (z - c)^2 - d;
sol = SolveAlways[{-11 - 2 x + x^2 - 4 y + y^2 - 6 z + z^2 == eq}, {x, y, z}]
eq /. sol // PolynomialForm[#, TraditionalOrder -> True] &

(* {{d -> 25, a -> 1, b -> 2, c -> 3}} *)
(* {(x-1)^2+(y-2)^2+(z-3)^2-25} *)

added 175 characters in body

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edited Feb 25, 2013 at 11:26

chyanog

15.8k
3
41
83

SolveAlways[{-11 - 2 x + x^2 - 4 y + y^2 - 6 z +  z^2 ==
 (x - a)^2 + (y - b)^2 + (z - c)^2 - 25}, {x, y, z}]
(*{{a -> 1, b -> 2, c -> 3}}*)

Updated:

SolveAlways[{-11 - 2 x + x^2 - 4 y + y^2 - 6 z + z^2 == 
(x - a)^2 + (y - b)^2 + (z - c)^2 - d}, {x, y, z}]

(*{{d -> 25, a -> 1, b -> 2, c -> 3}}*)

SolveAlways[{-11 - 2 x + x^2 - 4 y + y^2 - 6 z +  z^2 ==
 (x - a)^2 + (y - b)^2 + (z - c)^2 - 25}, {x, y, z}]

(*{{a -> 1, b -> 2, c -> 3}}*)

SolveAlways[{-11 - 2 x + x^2 - 4 y + y^2 - 6 z +  z^2 ==
 (x - a)^2 + (y - b)^2 + (z - c)^2 - 25}, {x, y, z}]
(*{{a -> 1, b -> 2, c -> 3}}*)

Updated:

SolveAlways[{-11 - 2 x + x^2 - 4 y + y^2 - 6 z + z^2 == 
(x - a)^2 + (y - b)^2 + (z - c)^2 - d}, {x, y, z}]

(*{{d -> 25, a -> 1, b -> 2, c -> 3}}*)

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created Feb 25, 2013 at 10:28

chyanog

15.8k
3
41
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