+118608 Do you want to know what shape it is? Looks like a circle to me. 
$$\\36x^2+36y^2-24x-12y=31\\
36x^2-24x+36y^2-12y=31\\
36(x^2-\frac{2x}{3}+y^2-\frac{1y}{3})=31\\
(x^2-\frac{2x}{3})+(y^2-\frac{1y}{3})=\frac{31}{36}\\
(x^2-\frac{2x}{3}+\frac{1}{9})+(y^2-\frac{1y}{3}+\frac{1}{36})=\frac{31}{36}+\frac{1}{9}+\frac{1}{36}\\
(x-\frac{1}{3})^2+(y-\frac{1}{6})^2=1\\$$
$$\\Circle:\qquad centre\;(\frac{1}{3},\frac{1}{6})\qquad radius=1\;unit$$
+26367 36x^2+36y^2-24x-12y=31
\(\begin{array}{rcll} 36x^2+36y^2-24x-12y &=& 31 \\ (36x^2-24x)+(36y^2-12y) &=& 31 \quad & | \quad : 36 \\\\ (x^2-\frac{2}{3}x)+(y^2-\frac{1}{3}y) &=& \frac{31}{36} \\ \\ (x-\frac{2}{6})^2-\frac{4}{36}+(y-\frac{1}{6})^2-\frac{1}{36} &=& \frac{31}{36} \\ \\ (x-\frac{1}{3})^2 +(y-\frac{1}{6})^2&=& \frac{31}{36} +\frac{4}{36}+\frac{1}{36} \\ \\ (x-\frac{1}{3})^2 +(y-\frac{1}{6})^2&=& 1 \\ \\ \end{array}\)
36X^2+36y^2-24x-12y=31
This is a circle with center
\( \left(\dfrac{1}{3} ,\; \dfrac{1}{6}\right)\)
and the radius = 1
+118608 Do you want to know what shape it is? Looks like a circle to me.
$$\\36x^2+36y^2-24x-12y=31\\
36x^2-24x+36y^2-12y=31\\
36(x^2-\frac{2x}{3}+y^2-\frac{1y}{3})=31\\
(x^2-\frac{2x}{3})+(y^2-\frac{1y}{3})=\frac{31}{36}\\
(x^2-\frac{2x}{3}+\frac{1}{9})+(y^2-\frac{1y}{3}+\frac{1}{36})=\frac{31}{36}+\frac{1}{9}+\frac{1}{36}\\
(x-\frac{1}{3})^2+(y-\frac{1}{6})^2=1\\$$
$$\\Circle:\qquad centre\;(\frac{1}{3},\frac{1}{6})\qquad radius=1\;unit$$
