Work Step by Step
If $B=0$ and $A $ and $C$ are not both zero, then the general equation of a conic has the form of $Ax^2+Cy^2+Dx+Ey+F=0(1)$ (a) When $AC=0$, then a conic defines a parabola. (b) When $AC \gt 0$, then a conic defines an ellipse and $A\ne C$ (c) When $AC \gt 0$, then a conic defines a Circle and $A=C$ (d) When $AC \lt 0$, then a conic defines a hyperbola. We have: $A=2,C=1$. Plug these values in Equation (1) to obtain: $AC=(2)(1)=2 \gt 0$,and $6 \ne 3$, so the conic represents an Ellipse.