## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

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: $A=1,B=-7,C=3$. Plug these values in Equation (1) to obtain: $B^2-4AC=(-7)^2-4(1)(3)=49-12=37 \gt 0$ so the conic represents a hyperbola.