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 $A=2,B=-3,C=4$, hence $B^2-4AC=(-3)^2-4(2)(4)=9-32=-23\lt0$, and $2\ne4$, thus it is an ellipse.