Puzzles - Crazy curves

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Crazy curves

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Except for the circle (which is shown for reference), on the other three curves, except where the curves cross an axis, all the points (x,y) have an interesting property. In fact this property holds for all the curves of this family for any power of x and y above 2. What is so special about the co-ordinates (x,y) of these points and why?

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Puzzles: Crazy curves

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