Question

Xy=1 in polar coordinates

Answer 1

`xy=1\iff (r\cos\theta)(r\sin\theta)=r^2\sin\theta\cos\theta=\frac12r^2\sin2\theta=1`

`\implies r^2=2\csc2\theta`

`\implies r=√(2\csc2\theta)`

where we ignore the second root and use the convention that
`r>0`.