Answer :
we have the equation
[tex]2x²+2y²-6x+4y+1=0[/tex]Group similar terms and move the constant term to the right side
[tex](2x^2-6x)+(2y^2+4y)=-1[/tex]Factor the leading coefficient on both terms of the left side
[tex]2(x^2-3x)+2(y^2+2y)=-1[/tex]Complete the square twice
[tex]2(x^2-3x+1.5^2)+2(y^2+2y+1)=-1+4.5+2[/tex]Rewrite as a perfect square
[tex]2(x-1.5)^2+2(y+1)^2=5.50[/tex]Divide both sides by 2
[tex]\begin{gathered} (x-1.5)^2+(y+1)^2=\frac{5.50}{2} \\ \\ (x-1.5)^2+(y+1)^2=2.75 \end{gathered}[/tex]we have the equation of a circle
therefore