The point \(P\) on the hyperbola \(xy=c^2\) is such that the tangent to the hyperbola at \(P\) passes through the focus of the parabola \(y^2=4ax\). Find the coordinates of \(P\) in terms of \(a\) and \(c\).

If \(P\) also lies on the parabola, prove that \(a^4=2c^4\), and calculate the acute angle between the tangents to the two curves at \(P\).