Question

Find a Cartesian equation for the curve and identify it: r²sin2θ = 1

Answer 1

Putting $sin2\theta=2 sin \theta \cdot cos \theta, \\ sin\theta= \frac{y}{r}\\ cos\theta=\frac{x}{r}\\ \implies 2xy=1\\ Hence \: xy=\frac{1}{2}\\ \mathfrak{ This \: equation \: is \: that \: of \: a \: hyperbola}$