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, $A=10,B=4,C=4$, hence, $B^2-4AC=(10)^4-4(4)(4)=100-64=36\gt0$ Thus, it is a hyperbola.