Work Step by Step
All conics' equations are in the form $Ax^2+Bxy+Cy^2+Dx+Ey+F=0$. In this the discriminant is $D=B^2-4AC$. Then we have $4$ cases: 1) $D\lt0,B=0,A=C$, then the conic is a circle 2) $D\lt0$ but $B\ne0$ or $A\ne C$, then it is an ellipse 3) $D=0$, then it is a parabola 4) $D\gt0$, then it is a hyperbola. Hence here $D=0^2-4(6)(-2)=48\gt0$, thus it is a hyperbola.