Question 1205414
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In this my post,  I want to notice that the problem is posed incorrectly.


Indeed, it says that  x, y ∈ Z,   which is  INCORRECT.


A circle with the center at rational point on a plane (in this problem - a circle with the center 
at integer point  (-2,5))  and the radius  2  can not contain any rational/integer point,  except trivial points
((0,5),  (-2,7),  (-4,5)  and  (-2,3).


The correct form is   x, y ∈ R.



Also,  keep in mind that the solution by @MathLover1 is  INCORRECT  and  IRRELEVANT.



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Edwin, it is somehow awkward for me to read and to comment what you wright on this your post as mccravyedwin.