Do you want to know what shape it is? Looks like a circle to me. 
$$\\36x^2+36y^2-24x-12y=31\\
36x^2-24x+36y^2-12y=31\\
36(x^2-\frac{2x}{3}+y^2-\frac{1y}{3})=31\\
(x^2-\frac{2x}{3})+(y^2-\frac{1y}{3})=\frac{31}{36}\\
(x^2-\frac{2x}{3}+\frac{1}{9})+(y^2-\frac{1y}{3}+\frac{1}{36})=\frac{31}{36}+\frac{1}{9}+\frac{1}{36}\\
(x-\frac{1}{3})^2+(y-\frac{1}{6})^2=1\\$$
$$\\Circle:\qquad centre\;(\frac{1}{3},\frac{1}{6})\qquad radius=1\;unit$$
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