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Other ways shift the terms containing x₀² and y₀² from the left-hand side of the equation

Posted 2 days ago
b^2 x x0 - b^2 x0^2 + a^2 y y0 - a^2 y0^2 == 0

How to simultaneously shift the terms containing x₀² and y₀² from the left-hand side of the equation,get the result as follows:What other good methods are there?

b^2 x x0 + a^2 y y0 == b^2 x0^2 + a^2 y0^2

The follows is my own method.

b^2 x x0 - b^2 x0^2 + a^2 y y0 - a^2 y0^2 == 0
% /.
 b^2 x x0 - m_.*b^2 x0^2 + a^2 y y0 - n_.*a^2 y0^2 == 0 :> 
  b^2 x x0 + a^2 y y0 == m*b^2 x0^2 + n*a^2 y0^2
POSTED BY: Bill Blair
3 Replies

Another way:

eqn = b^2 x x0 - b^2 x0^2 + a^2 y y0 - a^2 y0^2 == 0

With[{sides = 
   GroupBy[MonomialList[Subtract @@ eqn], FreeQ[x0^2 | y0^2]]},
 Total[Lookup[sides, True, {}]] == -Total[Lookup[sides, False, {}]]]
POSTED BY: Michael Rogers

One way is to use SubtractSides:

eq = b^2 x x0 - b^2 x0^2 + a^2 y y0 - a^2 y0^2 == 0;
terms = Total@Cases[eq[[1]], _.*x0^2 | _.*y0^2]
SubtractSides[eq, terms]
POSTED BY: Gianluca Gorni
Posted 1 day ago

Here is one alternative:

equ=b^2 x x0-b^2 x0^2+a^2 y y0-a^2 y0^2==0;
Select[First@equ,FreeQ[#,x0^2]&&FreeQ[#,y0^2]&]==-Select[First@equ,!FreeQ[#,x0^2]\[Or]!FreeQ[#,y0^2]&]
POSTED BY: Hans Milton
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