Polar equation and asymptotics of the hyperbolic spiral

A hyperbolic spiral is written in a parametric form as follows: \(x = \frac{\alpha}{t}\cos t\), \(y = \frac{\alpha}{t}\sin t\), where \(\alpha > 0\) is a constant and \(t\) varies from \(0\) to \(\infty\). Write the equation of this spiral in a polar coordinate system in the form \(r = r(\theta)\). Draw it schematically. Investigate the limit of \(x\), \(y\) and \(r\) as \(\theta \to 0\).