we have the equation
x^2 −4x+y^2 +2y=−4
step 1
Complete the squares
group terms
(x^2-4x)+(y^2+2y)=-4
(x^2-4x+4)+(y^2-2y+1)=-4+4+1
(x^2-4x+4)+(y^2-2y+1)=1
rewrite as perfect squares
(x-2)^2+(y-1)^2=1
the equation represent a circle with center at (2,1) and radius 1 unit
therefore
the answer is the option D