There is no sensible simplification.
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Yes. I assume you mean (x2 + y2) / (a2 + b2) = 1. Set all the variables to the same value - for example, all equal to one - and you have a valid solution.
It is x = 0.
X= plus or minus 1
It depends on what precisely the question is. One possible answer is that the quadratic expression has a value of 2 when x = 0.
'A' squared, plus 'B' squared, must equal 'C' squared, but only if the 'C' side is the hypotenuse (long side). A right (or left) triangle MUST have ONE 90-degree angle.