Question 1163779
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x 2 + y 2 + 4x - 6y + 23 = 0
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{{{x^2+4x+y^2-6y=-23}}}

Complete The Squares.

{{{x^2+4x+4+y^2-6y+9=-23+4+9}}}

{{{(x+2)^2+(y-3)^2=-10}}}----------------Not a circle.  Recheck my steps if you want in case any mistakes were made.