Chapter 13 - Conic Sections - 13.3 Conic Sections: Hyperbolas - 13.3 Exercise Set - Page 871: 35

Hyperbola

$x-\frac{3}{y}=0$ Rewrite the equation as shown below, $\begin{align} & x=\frac{3}{y} \\ & xy=3 \\ & xy-3=0 \end{align}$ Compare the equation $xy-3=0$ with the standard equation of a conic section: $A{{x}^{2}}+B{{y}^{2}}+Cxy+Dx+Ey+F=0$, Here, $C=1,F=-3$ Therefore, the graph of the equation is a hyperbola.