Answer
hyperbola.
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: $A=1,B=3,C=-2$.
Plug these values in Equation (1) to obtain: $B^2-4AC=3^4-4(1)(-2)=9+8=17\gt 0$, so it is a hyperbola.
