Two tangents are drawn from a point \(P\) to the circle \(x^2+y^2-2 x-4 y+4=0\), such that the angle between these tange…

Two tangents are drawn from a point \(P\) to the circle \(x^2+y^2-2 x-4 y+4=0\), such that the angle between these tangents is \(\tan ^{-1}\left(\frac{12}{5}\right)\) where \(\tan ^{-1}\left(\frac{12}{5}\right) \in(0, \pi)\) If the centre of the circle is denoted by \(C\) and these tangents touch the circle at points \(A\) and \(B\), then the ratio of the areas of \(\triangle P A B\) and \(\triangle C A B\) is:

[JEE Main 2021, 17 Mar (Shift 2)]