Question

Convert the Cartesian equation 2xy = 1 to a polar equation.

Answer 1

$\bf \textit{Double Angle Identities} \\\\ sin(2\theta)=2sin(\theta)cos(\theta)\\\\ -------------------------------\\\\ \begin{cases} x=rcos(\theta )\\ y=rsin(\theta ) \end{cases}\qquad 2xy=1\implies 2rcos(\theta )rsin(\theta )=1 \\\\\\ r^2\cdot 2cos(\theta )sin(\theta )=1\implies r^2\cdot sin(2\theta )=1$