Let \( PQ \) and \( MN \) be two straight lines touching the circle \( x^2 + y^2 - 4x - 6y - 3 = 0 \) at the points \( A \) and \( B \) respectively.
Let \( O \) be the centre of the circle and \( \angle AOB = \frac{\pi}{3} \). Then the locus of the point of intersection of the lines \( PQ \) and \( MN \) is:
