Answer
ellipse
Work Step by Step
The general equation of a conic in the form of $Ax^2+Bxy+Cy^2+Dx+Ey+F=0$
(i) defines a parabola if $B^2-4AC=0$
(ii) defines an ellipse if $B^2-4AC\lt0$ and $A\ne C$
(iii) defines a circle if $B^2-4AC\lt0$ and $A= C$
(iv) defines a hyperbola if $B^2-4AC\gt0$
Here $A=3,B=2,C=1$, hence $B^2-4AC=(2)^2-4(3)(1)=4-12=-8\lt0$ and $3\ne1, thus it is an ellipse.