Chapter 10 - Parametric Equations and Polar Coordinates - 10.3 Polar Coordinates - 10.3 Exercises - Page 706: 20

$$2xy =1$$ Rectangular hyperbola with center at $(0,0)$

Since \begin{align*} r^{2} \sin 2 \theta&=1\\ 2r^{2} \sin \theta\cos \theta &=1\\ 2(r\cos \theta )(r\sin \theta )&=1\\ 2xy&=1 \end{align*} Rectangular hyperbola with center at $(0,0)$