Answer
Ellipse
Work Step by Step
The general equation of a conic has the form of $Ax^2+Bxy+Cy^2+Dx+Ey+F=0~~(1)$
(a) When $B^2-4AC=0$, then a conic defines a parabola.
(b) When $B^2-4AC \lt 0$, then a conic defines an ellipse and $A\ne C$
(c) When $B^2-4AC \lt 0$, then a conic defines a parabola and $A=C$
(d) When $B^2-4AC \gt 0$, then a conic defines a hyperbola.
We have: $A=3,B=-2,C=1$.
Plug these values in Equation (1) to obtain:
$B^2-4AC=(-2)^2-4(3)(1)=4 -12=-8 \lt 0$, and $3 \ne 1$
so the conic represents an Ellipse.