The straight line \(x = 3\) intersects the circle \[ x^2 + y^2 - 8x - 10y - 9 = 0 \] at the points \(P\) and \(Q\).

Calculate

- the coordinates of \(P\) and \(Q\),
- the equations of the tangents at \(P\) and \(Q\),
- the coordinates of the point of intersection of the tangents.