## Precalculus (10th Edition)

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 $A=4,B=12,C=9$, hence $B^2-4AC=(12)^2-4(4)(9)=144-144=0$, thus it is a parabola.